论文标题
圆磨品种和混合霍奇模块的交叉配合物
Intersection complexes of toric varieties and mixed Hodge modules
论文作者
论文摘要
我们证明了混合Hodge模块类别中曲折品种的交点复合物的结构定理。该定理归因于伯恩斯坦，科万夫斯基和麦克弗森的基础复合物具有合理系数。作为推论，非脱晶曲面超表面的Euler特征hodge数量可以由Euler特征的小计数量以及Newton Polyhedra的组合数据确定。这是由Batyrev--Borisov隐式使用的。请注意，Danilov-Khovanskii给出了以牛顿Polyhedra为单位的Euler特征小怪兽数的公式。结构定理还暗示，在非分类折叠性超表面的规范压实中，重量过滤的分级过滤的分级过滤的hodge水平严格小于一般情况。这为由于Danilov-khovanskii而导致的非偏度曲曲面高空曲面的边界杂种数量的公式提供了另一个证明。
We prove the structure theorem of the intersection complexes of toric varieties in the category of mixed Hodge modules. This theorem is due to Bernstein, Khovanskii and MacPherson for the underlying complexes with rational coefficients. As a corollary the Euler characteristic Hodge numbers of non-degenerate toric hypersurface can be determined by the Euler characteristic subtotal Hodge numbers together with combinatorial data of Newton polyhedra. This is used implicitly in an explicit formula by Batyrev--Borisov. Note that a formula for the Euler characteristic subtotal Hodge numbers in terms of Newton polyhedra has been given by Danilov--Khovanskii. The structure theorem also implies that the graded quotients of the weight filtration on the middle cohomology of the canonical compactification of a non-degenerate toric hypersurface have Hodge level strictly smaller than the general case except for the middle weight. This gives another proof of a formula for the frontier Hodge numbers of non-degenerate toric hypersurfaces due to Danilov--Khovanskii.
