HOME

TheInfoList



Click Here for Items Related To - List of algebraic surfaces
OR:
List of algebraic surfaces on:   [Wikipedia]   [Google]   [Amazon]

This is a list of named
algebraic surface In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of di ...
s, compact complex surfaces, and families thereof, sorted according to their
Kodaira dimension In algebraic geometry, the Kodaira dimension ''κ''(''X'') measures the size of the canonical ring, canonical model of a projective variety ''X''. Igor Shafarevich, in a seminar introduced an important numerical invariant of surfaces with the ...
following
Enriques–Kodaira classification In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the modu ...
.


Kodaira dimension −∞


Rational surface In algebraic geometry, a branch of mathematics, a rational surface is a surface birational geometry, birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 1 ...
s

*
Projective plane In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do ...


Quadric surface In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension ''D'') in a -dimensional space, and it is de ...
s

*
Cone (geometry) A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines con ...
*
Cylinder A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infin ...
*
Ellipsoid An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface;  that is, a surface that may be defined as the ...
*
Hyperboloid In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by defo ...
*
Paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane ...
*
Sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
*
Spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has cir ...


Rational

cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than a ...
s

* Cayley nodal cubic surface, a certain cubic surface with 4 nodes *
Cayley's ruled cubic surface In differential geometry, Cayley's ruled cubic surface is the ruled cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algeb ...
*
Clebsch surface In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by and , all of whose 27 exceptional lines can be defined over the real numbers. The term Klein's icosahedral sur ...
or Klein icosahedral surface *
Fermat cubic In geometry, the Fermat cubic, named after Pierre de Fermat, is a surface defined by : x^3 + y^3 + z^3 = 1. \ Methods of algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynom ...
*
Monkey saddle In mathematics, the monkey saddle is the surface defined by the equation : z = x^3 - 3xy^2, \, or in cylindrical coordinates :z = \rho^3 \cos(3\varphi). It belongs to the class of saddle surfaces, and its name derives from the observation tha ...
* Parabolic conoid *
Plücker's conoid In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid; however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinde ...
*
Whitney umbrella frame, Section of the surface In geometry, the Whitney umbrella (or Whitney's umbrella, named after American mathematician Hassler Whitney, and sometimes called a Cayley umbrella) is a specific self-intersecting ruled surface placed in three dime ...


Rational

quartic surface In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An ''affine'' quartic surfac ...
s

*
Châtelet surface In algebraic geometry, a Châtelet surface is a rational surface studied by given by an equation :y^2-az^2=P(x), \, where ''P'' has degree 3 or 4. They are conic bundle In algebraic geometry, a conic bundle is an algebraic variety that app ...
s *
Dupin cyclide In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter are themselves examples of Dupin cyclides. They were discovered by (and named after) Charle ...
s, inversions of a cylinder, torus, or double cone in a sphere *
Gabriel's horn Gabriel's horn (also called Torricelli's trumpet) is a particular geometric figure that has infinite surface area but finite volume. The name refers to the Christian tradition where the archangel Gabriel blows the horn to announce Judgment Da ...
* Right circular conoid *
Roman surface In mathematics, the Roman surface or Steiner surface is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry. This mapping is not an immersion of the projective plane; ...
or Steiner surface, a realization of the
real projective plane In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has bas ...
in real
affine space In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties relate ...
* Tori, surfaces of revolution generated by a circle about a coplanar axis


Other rational surfaces in space

*
Boy's surface In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901. He discovered it on assignment from David Hilbert to prove that the projective plane ''could not'' be immersed in 3-space ...
, a sextic realization of the
real projective plane In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has bas ...
in real
affine space In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties relate ...
*
Enneper surface In differential geometry and algebraic geometry, the Enneper surface is a self-intersecting surface that can be described parametrically by: \begin x &= \tfrac u \left(1 - \tfracu^2 + v^2\right), \\ y &= \tfrac v \left(1 - \tfracv^2 + u^2\righ ...
, a nonic
minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...
*
Henneberg surface In differential geometry, the Henneberg surface is a non-orientable minimal surface named after Lebrecht Henneberg. It has parametric equation :\begin x(u,v) &= 2\cos(v)\sinh(u) - (2/3)\cos(3v)\sinh(3u)\\ y(u,v) &= 2\sin(v)\sinh(u) + (2/3)\sin( ...
, a minimal surface of degree 15 * Bour's minimal surface, a surface of degree 16 * Richmond surfaces, a family of minimal surfaces of variable degree


Other families of rational surfaces

*
Coble surface In algebraic geometry, a Coble surface was defined by to be a smooth rational projective surface with empty anti-canonical linear system , −K, and non-empty anti-bicanonical linear system , −2K, . An example of a Coble surface is th ...
s *
Del Pezzo surface In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with ample anticanonical divisor class. They are in some sense the opposite of surfaces of general ...
s, surfaces with an ample anticanonical divisor *
Hirzebruch surface In mathematics, a Hirzebruch surface is a ruled surface over the projective line. They were studied by . Definition The Hirzebruch surface \Sigma_n is the \mathbb^1-bundle, called a Projective bundle, over \mathbb^1 associated to the sheaf\mathca ...
s, rational ruled surfaces *
Segre surface In algebraic geometry, a Segre surface, studied by and , is an intersection of two quadrics in 4-dimensional projective space. They are rational surfaces isomorphic to a projective plane blown up in 5 points with no 3 on a line, and are del Pez ...
s, intersections of two quadrics in projective 4-space * Unirational surfaces of characteristic 0 *
Veronese surface In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics. It is named after Giu ...
, the
Veronese embedding In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics. It is named after ...
of the projective plane into projective 5-space *
White surface In algebraic geometry, a White surface is one of the rational surfaces in ''P'n'' studied by , generalizing cubic surface In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic s ...
s, the blow-up of the projective plane at _C_2 points by the linear system of degree-n curves through those points **
Bordiga surface In algebraic geometry, a Bordiga surface is a certain sort of rational surface of degree 6 in ''P''4, introduced by Giovanni Bordiga. A Bordiga surface is isomorphic to the projective plane blown up in 10 points, the embedding into ''P''4 is ...
s, the White surfaces determined by families of quartic curves


Non-rational ruled surfaces


Class VII surfaces

* Vanishing second
Betti number In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicia ...
: **
Hopf surface In complex geometry, a Hopf surface is a compact complex surface obtained as a quotient of the complex vector space (with zero deleted) \Complex^2\setminus \ by a free action of a discrete group. If this group is the integers the Hopf surface is cal ...
s ** Inoue surfaces; several other families discovered by Inoue have also been called "Inoue surfaces" * Positive second
Betti number In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicia ...
: ** Enoki surfaces ** Inoue–Hirzebruch surfaces **
Kato surface In mathematics, a Kato surface is a compact complex surface with positive first Betti number that has a global spherical shell. showed that Kato surfaces have small analytic deformations that are the blowups of primary Hopf surfaces at a finite num ...
s


Kodaira dimension 0


K3 surface In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth proper geometrically connected alg ...
s

*
Kummer surface In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety o ...
s **
Tetrahedroid In algebraic geometry, a tetrahedroid (or tétraédroïde) is a special kind of Kummer surface In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal ...
s, special Kummer surfaces **
Wave surface In mathematics, Fresnel's wave surface, found by Augustin-Jean Fresnel in 1822, is a quartic surface describing the propagation of light in an optically biaxial crystal. Wave surfaces are special cases of tetrahedroids which are in turn special ...
, a special tetrahedroid *
Plücker surface In algebraic geometry, a Plücker surface, studied by , is a quartic surface in 3-dimensional projective space with a double line and 8 nodes. Construction For any quadric line complex In algebraic geometry, a line complex is a 3-fold given by t ...
s, birational to Kummer surfaces *
Weddle surface In algebraic geometry, a Weddle surface, introduced by , is a quartic surface in 3-dimensional projective space, given by the locus of vertices of the family of cones passing through 6 points in general position. Weddle surfaces have 6 nodes an ...
s, birational to Kummer surfaces * Smooth
quartic surface In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An ''affine'' quartic surfac ...
s * Supersingular K3 surfaces


Enriques surface In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity ''q'' = 0 and the canonical line bundle ''K'' is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex n ...
s

*
Reye congruence In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity ''q'' = 0 and the canonical line bundle ''K'' is non-trivial but has trivial square. Enriques surfaces are all projective (and therefore Kähler over the complex n ...
s, the locus of lines that lie on two out of three general quadric surfaces in projective space


Abelian surface In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic via the Riemann bi ...
s

* ''Horrocks–Mumford surfaces'', surfaces of degree 10 in projective 4-space that are the zero locus of sections of the rank-two
Horrocks–Mumford bundle In algebraic geometry, the Horrocks–Mumford bundle is an indecomposable rank 2 vector bundle on 4-dimensional projective space ''P''4 introduced by . It is the only such bundle known, although a generalized construction involving Paley graphs prod ...


Other classes of dimension-0 surfaces

* Non-classical Enriques surfaces, a variation on the notion of Enriques surfaces that only exist in characteristic two *
Hyperelliptic surface In mathematics, a hyperelliptic surface, or bi-elliptic surface, is a surface whose Albanese morphism is an elliptic fibration. Any such surface can be written as the quotient of a product of two elliptic curves by a finite abelian group. Hyperel ...
s or bielliptic surfaces; ''quasi-hyperelliptic surfaces'' are a variation of this notion that exist only in characteristics two and three *
Kodaira surface In mathematics, a Kodaira surface is a compact space, compact algebraic surface, complex surface of Kodaira dimension 0 and odd first Betti number. The concept is named after Kunihiko Kodaira. These are never algebraic, though they have non-constan ...
s


Kodaira dimension 1

*
Dolgachev surface In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by . They can be used to give examples of an infinite family of homeomorphic simply connected compact 4-manifolds, no two of which are diffeomorphic. P ...
s


Kodaira dimension 2 (

surfaces of general type In algebraic geometry, a surface of general type is an algebraic surface with Kodaira dimension 2. Because of Algebraic geometry and analytic geometry#Chow.27s theorem, Chow's theorem any compact complex manifold of dimension 2 and with Kodaira ...
)

*
Barlow surface In mathematics, a Barlow surface is one of the complex surfaces introduced by . They are simply connected surfaces of general type with ''pg'' = 0. They are homeomorphic but not diffeomorphic to a projective plane blown up in 8 points. T ...
s *
Beauville surface In mathematics, a Beauville surface is one of the surfaces of general type introduced by . They are examples of "fake quadrics", with the same Betti numbers as quadric surfaces. Construction Let ''C''1 and ''C''2 be smooth curves with genera ''g' ...
s * Burniat surfaces *
Campedelli surface In mathematics, a Campedelli surface is one of the surfaces of general type introduced by Campedelli. Surfaces with the same Hodge number In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of ...
s; surfaces of general type with the same
Hodge number In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohom ...
s as Campedelli surfaces are called ''numerical Campidelli surfaces'' *
Castelnuovo surface In mathematics, a Castelnuovo surface is a surface of general type such that the canonical bundle is very ample and such that ''c''12 = 3''pg'' − 7. Guido Castelnuovo Guido Castelnuovo (14 August 1865 – 27 April 1952 ...
s * Catanese surfaces *
Fake projective plane In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are not isomorphic to it. Such objects are always algebraic surfaces of general ...
s or Mumford surfaces, surfaces with the same
Betti number In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicia ...
s as projective plane but not isomorphic to it *
Fano surface In algebraic geometry, a Fano surface is a surface of general type (in particular, not a Fano variety) whose points index the lines on a non-singular cubic threefold. They were first studied by . Hodge diamond: Fano surfaces are perhaps the s ...
of lines on a non-singular 3-fold; sometimes, this term is taken to mean del Pezzo surface *
Godeaux surface In mathematics, a Godeaux surface is one of the surfaces of general type introduced by Lucien Godeaux in 1931. Other surfaces constructed in a similar way with the same Hodge numbers are also sometimes called Godeaux surfaces. Surfaces with the sam ...
s; surfaces of general type with the same
Hodge number In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohom ...
s as Godeaux surfaces are called ''numerical Godeaux surfaces'' *
Horikawa surface In mathematics, a Horikawa surface is one of the surfaces of general type introduced by Horikawa. These are surfaces with ''q'' = 0 and ''pg'' = ''c''12/2 + 2 or ''c''12/2 + 3/2 (which implies that they a ...
s *
Todorov surface In algebraic geometry, a Todorov surface is one of a class of surfaces of general type introduced by for which the conclusion of the Torelli theorem In mathematics, the Torelli theorem, named after Ruggiero Torelli, is a classical result of alg ...
s


Families of surfaces with members in multiple classes

* Surfaces that are also
Shimura varieties In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are no ...
: **
Hilbert modular surface In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular varie ...
s **
Humbert surface In algebraic geometry, a Humbert surface, studied by , is a surface (mathematics), surface in the moduli space of principally polarized abelian surfaces consisting of the surfaces with a symmetric endomorphism of some fixed discriminant. References ...
s **
Picard modular surface In mathematics, a Picard modular surface, studied by , is a complex surface constructed as a quotient of the unit ball in C2 by a Picard modular group. Picard modular surfaces are some of the simplest examples of Shimura varieties and are sometimes ...
s ** Shioda modular surfaces *
Elliptic surface In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed fi ...
s, surfaces with an elliptic fibration; ''quasielliptic surfaces'' constitute a modification this idea that occurs in finite characteristic **
Raynaud surface In mathematics, a Raynaud surface is a particular kind of algebraic surface that was introduced in and named for . To be precise, a Raynaud surface is a quasi-elliptic surface over an algebraic curve of genus ''g'' greater than 1, such that all fi ...
s and generalized Raynaud surfaces, certain quasielliptic counterexamples to the conclusions of the
Kodaira vanishing theorem In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices ''q'' > 0 are automatically zero. The implica ...
* Exceptional surfaces, surfaces whose Picard number achieve the bound set by the central Hodge number ''h''1,1 *
Kähler surface Kähler may refer to: ;People * Alexander Kähler (born 1960), German television journalist * Birgit Kähler (born 1970), German high jumper *Erich Kähler (1906–2000), German mathematician *Heinz Kähler (1905–1974), German art historian and a ...
s, complex surfaces with a Kähler metric; equivalently, surfaces for which the first Betti number ''b''1 is even *
Minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces that ...
s, surfaces that can't be obtained from another by blowing up at a point; they have no connection with the minimal surfaces of differential geometry *
Nodal surface In algebraic geometry, a nodal surface is a surface in (usually complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex ...
s, surfaces whose only singularities are nodes ** Cayley's nodal cubic, which has 4 nodes ** Kummer surfaces, quartic surfaces with 16 nodes **
Togliatti surface In algebraic geometry, a Togliatti surface is a nodal surface of degree five with 31 Node (algebraic geometry), nodes. The first examples were constructed by . proved that 31 is the maximum possible number of nodes for a surface of this degree, ...
, a certain quintic with 31 nodes **
Barth surface __NOTOC__ In algebraic geometry, a Barth surface is one of the complex nodal surfaces in 3 dimensions with large numbers of double points found by . Two examples are the Barth sextic of degree 6 with 65 double points, and the Barth decic of degre ...
s, referring to a certain sextic with 65 nodes and decic with 345 nodes **
Labs surface In mathematics, the Labs septic surface is a degree-7 ( septic) nodal surface with 99 nodes found by . As of 2015, it has the largest known number of nodes of a degree-7 surface, though this number is still less than the best known upper bound of 1 ...
, a certain septic with 99 nodes **
Endrass surface In algebraic geometry, an Endrass surface is a nodal surface of degree 8 with 168 real nodes, found by . , it remained the record-holder for the most number of real nodes for its degree; however, the best proven upper bound, 174, does not match t ...
, a certain surface of degree 8 with 168 nodes **
Sarti surface In algebraic geometry, a Sarti surface is a degree-12 nodal surface with 600 nodes, found by . The maximal possible number of nodes of a degree-12 surface is not known (as of 2015), though Yoichi Miyaoka showed that it is at most 645. Sarti has ...
, a certain surface of degree 12 with 600 nodes * Quotient surfaces, surfaces that are constructed as the
orbit space In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces *
Zariski surface In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic ''p'' > 0 such that there is a dominant inseparable map of degree ''p'' from the projective plane to the surface. In particu ...
s, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane


See also

*
Enriques–Kodaira classification In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the modu ...
*
List of surfaces This is a list of surfaces, by Wikipedia page. ''See also List of algebraic surfaces, List of curves, Riemann surface.'' Minimal surfaces * Catalan's minimal surface * Costa's minimal surface * Catenoid * Enneper surface * Gyroid * Helicoid * Lid ...


References

* ''Compact Complex Surfaces'' by Wolf P. Barth, Klaus Hulek, Chris A.M. Peters, Antonius Van de Ven * ''Complex algebraic surfaces'' by Arnaud Beauville, {{isbn, 0-521-28815-0


External links

* Mathworld has a long list o
algebraic surfaces
with pictures. * Some mor
pictures of algebraic surfaces
especially ones with many nodes.
Pictures
of algebraic surfaces by Herwig Hauser.
Free program SURFER
to visualize algebraic surfaces in real-time, including a user gallery.
Algebraic surfaces In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of di ...