Journal ArticleDOI
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
Michel Brion,Michèle Vergne +1 more
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In this paper, the Riemann-Roch formula for the Todd class of complete simplicial toric varieties has been proposed, which has been used for enumeration of lattice points in convex lattice polytopes.Abstract:
Introduction. The theory of toric varieties establishes a now classical connection between algebraic geometry and convex polytopes. In particular, äs observed by Danilov in the seventies, finding a closed formula for the Todd class of complete toric varieties would have important consequences for enumeration of lattice points in convex lattice polytopes. Since then, a number of such formulas have been proposed; see [M], [Pl], [P2] The Todd class of complete simplicial toric varieties is computed in [G-G-K], using the Riemann-Roch formula of T. Kawasaki [Ka].read more
Citations
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Equivariant cohomology, Koszul duality, and the localization theorem
TL;DR: In this paper, the authors considered the action of a compact Lie group K on a space X and gave a description of equivariant homology and intersection homology in terms of Equivariant geometric cycles.
An Algorithmic Theory of Lattice Points in Polyhedra
TL;DR: In this paper, a survey of lattice points in rational polyhedra is presented, including relations to the theory of toric varieties and relations to classical and higher-dimensional Dedekind sums, complexity of Presburger arithmetic, and efficient computations with rational functions.
Journal ArticleDOI
Equivariant Chow groups for torus actions
TL;DR: In this article, the authors study Edidin and Graham's equivariant Chow groups in the case of torus actions and obtain a presentation of the Chow ring of any smooth, projective spherical variety.
Journal ArticleDOI
Residue formulae, vector partition functions and lattice points in rational polytopes
Michel Brion,Michèle Vergne +1 more
TL;DR: In this article, the sum of values of a polynomial function at all lattice points of a rational convex polytope is expressed in terms of the variation of the integral of the function over the deformed polytopes.
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On the Spectrum of the Equivariant Cohomology Ring
Mark Goresky,Robert MacPherson +1 more
TL;DR: In this paper, the affine scheme associated with the equivariant cohomology is often an arrangement of linear subspaces of the vector space of a complex projective algebraic variety.
References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Journal ArticleDOI
The moment map and equivariant cohomology
TL;DR: In this article, the authors propose a solution to solve the problem of spamming, which is called spamming-based spamming.$$$/$/$/$/$$
Posted Content
The Homogeneous coordinate ring of a toric variety, revised version
TL;DR: In this paper, an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety" is presented.
BookDOI
The topology of torus actions on symplectic manifolds
TL;DR: The Topology of Torus Actions on Symplectic Manifolds as mentioned in this paper is an extended version of the first edition of the Torus Action on Symmlectic manifolds published in 1991.