论文标题
节点射弹性曲面的分部定理
A Division Theorem for Nodal Projective Hypersurfaces
论文作者
论文摘要
令$ v_ {n，d} $为$ \ m athbb {p}^n（\ mathbb {c}）$的高度$ d $的多种方程式，其奇异性并不比简单节点差。我们证明轨道映射$ g'= sl_ {n+1}（\ mathbb {c}）\ to v_ {n，d} $，$ g \ g \ mapsto g \ cdot s_0 $，$ s_0 \ in v_ {n，d} $在$ n> 1 $ n> 1 $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ n> $ ge $（n，d）\ neq（2,3）$。结果，地图的leray-serre光谱序列从$ v_ {n，d} $到同型商$（v_ {n，d}）_ {hg'} $在$ e_2 $上degenerates $ degenerate in $ e_2 $，因此提供了点映射$ v_ $ v_ $ v_/d，商$ v_ {n，d}/g'$存在。我们表明，当$ d> n+1 $ $时，后者就是这种情况。
Let $V_{n,d}$ be the variety of equations for hypersurfaces of degree $d$ in $\mathbb{P}^n(\mathbb{C})$ with singularities not worse than simple nodes. We prove that the orbit map $G'=SL_{n+1}(\mathbb{C}) \to V_{n,d}$, $g\mapsto g\cdot s_0$, $s_0\in V_{n,d}$ is surjective on the rational cohomology if $n>1$, $d\geq 3$, and $(n,d)\neq (2,3)$. As a result, the Leray-Serre spectral sequence of the map from $V_{n,d}$ to the homotopy quotient $(V_{n,d})_{hG'}$ degenerates at $E_2$, and so does the Leray spectral sequence of the quotient map $V_{n,d}\to V_{n,d}/G'$ provided the geometric quotient $V_{n,d}/G'$ exists. We show that the latter is the case when $d>n+1$.
