Families of K-3 Surfaces
Families of K-3 Surfaces
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K-3 曲面族
作者：
A. Mayer
设V是一个二维紧致复流形.称V为K-3曲面，如果：a）V的不规则性q = dim H 1（V，θ）为零，B）V的第一Chern类c 1为零.这样一个曲面的（全纯2-形式的）标准层K是平凡的，因为q = 0意味着陈类映射c x：Pic（V）→ H2（V，Z）是单射的：因此V有一个无处为零的全纯2-形式。
Let V be a 2-dimensional compact complex manifold. V is called a K-3 surface if : a) the irregularity q = dim H1(V, θ) of V vanishes and b) the first Chern class c1 of V vanishes. The canonical sheaf (of holo-morphic 2-forms) K of such a surface is trivial, since q = 0 implies that the Chern class map c x : Pic (V) → H2(V, Z) is injective : thus V has a nowhere zero holomorphic 2-form.