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arXiv · alg-geom/9302003

Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes

Sacha Sardo-Infirri
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Abstract

A simple convex lattice polytope $\Box$ defines a torus-equivariant line bundle $\LB$ over a toric variety $\XB.$ Atiyah and Bott's Lefschetz fixed-point theorem is applied to the torus action on the $d''$-complex of $\LB$ and information is obtained about the lattice points of $\Box$. In particular an explicit formula is derived, computing the number of lattice points and the volume of $\Box$ in terms of geometric data at its extreme points. We show this to be equivalent the results of Brion \cite{brion} and give an elementary convex geometric interpretation by performing Laurent expansions similar to those of Ishida \cite{ishida}.

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BibTeXRIS

Sacha Sardo-Infirri. 1993-02-09. Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes. https://arxiv.org/abs/alg-geom/9302003

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