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1. CMB 2005 (vol 48 pp. 414)

Kaveh, Kiumars
 Vector Fields and the Cohomology Ring of Toric Varieties Let \$X\$ be a smooth complex projective variety with a holomorphic vector field with isolated zero set \$Z\$. From the results of Carrell and Lieberman there 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 projective toric 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 filtration and the polytope algebra of \$X\$. Keywords:Toric variety, torus action, cohomology ring, simple polytope,, polytope algebraCategories:14M25, 52B20

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