论文标题
组合交点的过滤并分子的不变性
Filtrations on combinatorial intersection cohomology and invariants of subdivisions
论文作者
论文摘要
在混合霍奇理论中的定义中，我们定义了粉丝组合交点共同体的体重过滤和单肌量过滤。 These filtrations give a natural definition of the multivariable invariants of subdivisions of polytopes, lattice polytopes and fans, namely the mixed $h$-polynomial, the refined limit mixed $h^*$-polynomial, and the mixed $cd$-index, defined by Katz--Stapledon and Dornian--Katz--Tsang.以前，只有精制的限制混合$ h^*$ - 多项式具有几何解释，该解释来自Schönhypersurface的共同体的过滤。因此，我们使用Karu的相对硬Lefschetz定理对Katz和Stapledon的混合$ h $ polynomial概括了阳性结果。
Motivated by definitions in mixed Hodge theory, we define the weight filtration and the monodromy weight filtration on the combinatorial intersection cohomology of a fan. These filtrations give a natural definition of the multivariable invariants of subdivisions of polytopes, lattice polytopes and fans, namely the mixed $h$-polynomial, the refined limit mixed $h^*$-polynomial, and the mixed $cd$-index, defined by Katz--Stapledon and Dornian--Katz--Tsang. Previously, only the refined limit mixed $h^*$-polynomial had a geometric interpretation, which came from filtrations on the cohomology of a schön hypersurface. Consequently, we generalize a positivity result on the mixed $h$-polynomial by Katz and Stapledon using the relative hard Lefschetz theorem of Karu.
