In mathematics, a Inoue–Hirzebruch surface is a
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 system, a system composed of many components which may interact with each ...
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
with no
meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset ''D'' of the complex plane is a function that is holomorphic on all of ''D'' ''except'' for a set of isolated points, which are ''poles'' of the function. ...
s introduced by . They have
Kodaira dimension
In algebraic geometry, the Kodaira dimension measures the size of the canonical model of a projective variety .
Soviet mathematician Igor Shafarevich in a seminar introduced an important numerical invariant of surfaces with the notation . ...
κ = −∞, and are non-algebraic
surfaces of class VII with 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 ...
. studied some higher-dimensional analogues.
See also
*
List of algebraic surfaces
This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification.
Kodaira dimension −∞
Rational surfaces
* Projective plane Qu ...
References
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{{DEFAULTSORT:Inoue-Hirzebruch surface
Complex surfaces