论文标题
交叉路口的共同体和Severi的品种
Intersection cohomology and Severi's varieties
论文作者
论文摘要
令$ x ^{2n} \ subseteq \ mathbb {p} ^n $为平滑的投射品种。考虑本地系统的交点共同体学$ r^{2n-1}π{_*} \ Mathbb {q} $，其中$π$表示来自$ x^{2n} $的通用超平面家族的投影，到$ {我们研究了相交共同体学复杂$ ic（r ^{2n-1}π{_*} \ mathbb {q}）$的共同体，上面是Severi多样性的点，参数化nodal HyperSurfaces的参数化，其nodal hyodal hydersurface在$ mathbb nodal hydersurface上施加了独立的线性条件，从而使$ \ nath $ \ mathbb node nodal nodal hyodection nodal Hypersurface a in Math $ \ mathbb ^p。
Let $X^{2n}\subseteq \mathbb{P} ^N$ be a smooth projective variety. Consider the intersection cohomology complex of the local system $R^{2n-1}π{_*}\mathbb{Q}$, where $π$ denotes the projection from the universal hyperplane family of $X^{2n}$ to ${(\mathbb{P} ^N)}^{\vee}$. We investigate the cohomology of the intersection cohomology complex $IC(R^{2n-1}π{_*}\mathbb{Q})$ over the points of a Severi's variety, parametrizing nodal hypersurfaces, whose nodes impose independent conditions on the very ample linear system giving the embedding in $\mathbb{P} ^N$.
