论文标题
关于孤立奇点解决的拓扑，ii
On the topology of a resolution of isolated singularities, II
论文作者
论文摘要
让$ y $成为带有孤立奇点的尺寸$ n $的复杂投影量，$π：x \ t y $ y $ singultions的分辨率，$ g：=π^{ - 1} \ left（\ rm {sing}（y）（y）（y）\ right）$。从分解定理中，一个人知道地图$ h^{k-1}（g）\ to h^k（y，y，y \ backslash {\ rm {sing}}（y））$ n $ n $。同样，相反，假设一个消失的人可以在几页中证明$π$的分解定理。本文的目的是展示消失的直接证明。结果，它遵循了$π$的完整和简短的分解定理，仅涉及普通的共同体。
Let $Y$ be a complex projective variety of dimension $n$ with isolated singularities, $π:X\to Y$ a resolution of singularities, $G:=π^{-1}\left(\rm{Sing}(Y)\right)$ the exceptional locus. From the Decomposition Theorem one knows that the map $H^{k-1}(G)\to H^k(Y,Y\backslash {\rm{Sing}}(Y))$ vanishes for $k>n$. It is also known that, conversely, assuming this vanishing one can prove the Decomposition Theorem for $π$ in few pages. The purpose of the present paper is to exhibit a direct proof of the vanishing. As a consequence, it follows a complete and short proof of the Decomposition Theorem for $π$, involving only ordinary cohomology.
