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In mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number. 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 ''P''n 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. ==References== * – the standard reference book for compact complex surfaces * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kodaira surface」の詳細全文を読む スポンサード リンク
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