关于Extremal Ray的除子型收缩

摘要

设X是定义在复数域上的n维光滑射影簇且它的典范除子Kx不是数字有效的,A是X上的一个ample除子.本文详细研究了由Kx+(n-k)A确定的关于X的除子型收缩映射(1≤k≤n-1),对其例外集的结构作了比较完整的分类.特别地,当1≤k≤3时,即得到Fujita,Sommese等人的相关结果.%Let X be an n-dimensional smooth projective variety with the canonical divisor Kx not nef. Let f: X → Y be the divisorial type contraction of an extremal ray with the supporting function Kx +(n-k)A for some ample A ∈ Pic(X) and some integer 1 ≤ k ≤ n-1. Some classifications for the exceptional locus of f are given.