Equivariant Chow cohomology of toric varieties
نویسندگان
چکیده
منابع مشابه
Equivariant Chow cohomology of toric varieties
We show that the equivariant Chow cohomology ring of a toric variety is naturally isomorphic to the ring of integral piecewise polynomial functions on the associated fan. This gives a large class of singular spaces for which localization holds in equivariant Chow cohomology with integer coefficients. We also compute the equivariant Chow cohomology of toric prevarieties and general complex hyper...
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Abstract. For a toric variety XΣ determined by a polyhedral fan Σ ⊆ N , Payne shows that the equivariant Chow cohomology is the Sym(N)–algebra C(Σ) of integral piecewise polynomial functions on Σ. We use the CartanEilenberg spectral sequence to analyze the associated reflexive sheaf C(Σ) on PQ(N), showing that the Chern classes depend on subtle geometry of Σ and giving criteria for the splittin...
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Let X be a complete nonsingular toric variety. In this lecture, we will descibe H∗ TX. First we recall some basic notions about toric varieties. Let T be an n-dimensional torus with character group M , and let N = HomZ(M,Z) be the dual lattice. Then X = X(Σ), for a complete nonsingular fan Σ. That is, Σ is a collection of cones σ in NR = N ⊗ZR such that two cones meet along a face of each; each...
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We compute the Chow groups and Fulton–MacPherson’s operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2006
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2006.v13.n1.a3