|
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 appears as a solution of a Cartesian equation of the form : X^2 + aXY + b Y^2 = P (T).\, Theoretically, it can be considered as a Severi–Brauer surface, or more precisely as ...s. References * * {{DEFAULTSORT:Chatelet Surface Algebraic surfaces Complex surfaces ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 10 or so classes of surface in the Enriques–Kodaira classification of complex surfaces, and were the first surfaces to be investigated. Structure Every non-singular rational surface can be obtained by repeatedly blowing up a minimal rational surface. The minimal rational surfaces are the projective plane and the Hirzebruch surfaces Σ''r'' for ''r'' = 0 or ''r'' ≥ 2. Invariants: The plurigenera are all 0 and the fundamental group is trivial. Homological mirror symmetry#Hodge diamond, Hodge diamond: where ''n'' is 0 for the projective plane, and 1 for Hirzebruch surfaces and greater than 1 for other rational surfaces. The Picard group is the odd unimodular lattice I1,''n'', except for the Hirzebruch surfaces Σ2''m'' when it is the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Bundle
In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution of a Cartesian equation of the form : X^2 + aXY + b Y^2 = P (T).\, Theoretically, it can be considered as a Severi–Brauer surface, or more precisely as a Châtelet surface. This can be a double covering of a ruled surface. Through an isomorphism, it can be associated with a symbol (a, P) in the second Galois cohomology of the field k. In fact, it is a surface with a well-understood divisor class group and simplest cases share with Del Pezzo surfaces the property of being a rational surface. But many problems of contemporary mathematics remain open, notably (for those examples which are not rational) the question of unirationality. A naive point of view To write correctly a conic bundle, one must first reduce the quadratic form of the left hand side. Thus, after a harmless change, it has a simple expression like : X^2 - aY^2 = P (T). \, In a second step, it should be placed in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal De Théorie Des Nombres De Bordeaux
The ''Journal de Théorie des Nombres de Bordeaux'' is a triannual peer-reviewed open-access scientific journal covering number theory and related topics. It was established in 1989 and is published by the Institut de Mathématiques de Bordeaux on behalf of the Société Arithmétique de Bordeaux. The editor-in-chief is Denis Benois (University of Bordeaux). Abstracting and indexing The journal is abstracted and indexed in Current Contents/Physical, Chemical & Earth Sciences, Zentralblatt MATH, Mathematical Reviews, Science Citation Index Expanded, and Scopus. According to the ''Journal Citation Reports'', the journal has a 2015 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 0.294. References External links * {{DEFAULTSORT:Journal de Theorie des N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 dimension four as a smooth manifold. The theory of algebraic surfaces is much more complicated than that of algebraic curves (including the compact Riemann surfaces, which are genuine surfaces of (real) dimension two). Many results were obtained, however, in the Italian school of algebraic geometry, and are up to 100 years old. Classification by the Kodaira dimension In the case of dimension one varieties are classified by only the topological genus, but dimension two, the difference between the arithmetic genus p_a and the geometric genus p_g turns to be important because we cannot distinguish birationally only the topological genus. Then we introduce the irregularity for the classification of them. A summary of the results (in det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
