Fixed Points of Torus Action and Cohomology Ring of Toric Varieties

Details Fixed Points of Torus Action and Cohomology Ring of Toric Varieties Fixed Points of Torus Action and Cohomology Ring of Toric Varieties

2003-08-27

arxiv.org/abs/math/0308266v1

Mathematics

Algebraic Geometry

15 pages, LaTex file, 2 .eps figures, 1 .eepic figure

Scientific paper

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.

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