Complex surfaces

Kodaira surface

In mathematics, a Kodaira surface is a compact 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-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite groups of orders 2, 3, 4, or 6, and which have non-trivial canonical bundles. The secondary Kodaira surfaces have the same relation to primary ones that Enriques surfaces have to K3 surfaces, or bielliptic surfaces have to abelian surfaces. Invariants: If the surface is the quotient of a primary Kodaira surface by a group of order k = 1,2,3,4,6, then the plurigenera Pn are 1 if n is divisible by k and 0 otherwise. Hodge diamond: Examples: Take a non-trivial line bundle over an elliptic curve, remove the zero section, then quotient out the fibers by Z acting as multiplication by powers of some complex number z.This gives a primary Kodaira surface. (Wikipedia).

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Complex surfaces 6: Kodaira dimensions 1 and 2

In this lecture we continue the overview of complex projective urfaces by discussing those of Kodaira dimensions 1 and 2. The surfaces of dimension 1 are all elliptic surfaces with a map onto a curve whose fibers are mostly elliptic curves. We describe Kodaira's classification of the poss

From playlist Algebraic geometry: extra topics

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Complex surfaces 5: Kodaira dimension 0

This talk is an informal survey of the complex projective surfaces of Kodaira number 0. We first explain why there are 4 types of such surfaces (Enriques, K3, hyperelliptic, and abelian) and then give a few examples of each type.

From playlist Algebraic geometry: extra topics

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Hsueh-Yung Lin: On the existence of algebraic approximations of compact Kähler manifolds

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From playlist Analysis and its Applications

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From playlist Location by City - Tokyo - J Utah

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From playlist Art of Asia | Art History | Khan Academy

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From playlist Location by City - Tokyo - J Utah

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From playlist Location by City - Tokyo - J Utah

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From playlist Algebraic and Complex Geometry

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From playlist Algebraic and Complex Geometry

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Alessandra Sarti: Topics on K3 surfaces - Lecture 1: K3 surfaces in the Enriques Kodaira...

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From playlist Algebraic and Complex Geometry

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From playlist Algebraic and Complex Geometry

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Complex surfaces 4: Ruled surfaces

This talk gives an informal survey of ruled surfaces and their role in the Enriques classification. We give a few examples of ruled surfaces, summarize the basic invariants of surfaces, and sketch how one classifies the surfaces of Kodaira dimension minus infinity.

From playlist Algebraic geometry: extra topics

Related pages

Abelian surface | Algebraic surface | Compact space | K3 surface | Kunihiko Kodaira | Betti number | Enriques surface | Kodaira dimension