Vector Fields and the Cohomology Ring of Toric Varieties

Canadian mathematical bulletin

关键词: Toric variety;    torus action;    cohomology ring;    simple polytope;    polytope algebra;   

DOI  :  10.4153/CMB-2005-039-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $X$ be a smooth complexprojective variety with a holomorphic vector field with isolatedzero set $Z$. From the results of Carrell and Liebermanthere exists a filtration$F_0 subset F_1 subset cdots$ of $A(Z)$, the ring of$c$-valued functions on $Z$, such that $Gr A(Z) cong H^*(X,c)$ as graded algebras. In this note, for a smooth projectivetoric variety and a vector field generated by the action of a$1$-parameter subgroup of the torus, we work out this filtration.Our main result is an explicit connection between this filtrationand the polytope algebra of $X$.

【 授权许可】

Unknown