Fixed Points of Torus Action and Cohomology Ring of Toric Varieties
Algebraic Geometry
2007-05-23 v1
Abstract
Let X be a smooth simplicial toric variety. Let Z be the set of T-fixed points of X. We construct a filtration for A(Z), the ring of complex-valued functions on Z, such that Gr A(Z) is isomorphic to the cohomology algebra of X. This is the explanation of the general results of Carrell and Liebermann on the cohomology of T-varities, in the case of toric varieties. We give an explicit isomorphism between Gr A(Z) and Brion's description of the polytope algebra.
Cite
@article{arxiv.math/0308266,
title = {Fixed Points of Torus Action and Cohomology Ring of Toric Varieties},
author = {Kiumars Kaveh},
journal= {arXiv preprint arXiv:math/0308266},
year = {2007}
}
Comments
15 pages, LaTex file, 2 .eps figures, 1 .eepic figure