Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes

dc.creatorSardo-Infirri, Sacha
dc.date1993-02-09
dc.date.accessioned2026-07-07T09:05:48Z
dc.date.available2026-07-07T09:05:48Z
dc.descriptionA 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}.
dc.description29 pages, latex 2.09
dc.identifierhttps://arxiv.org/abs/alg-geom/9302003
dc.identifierhttp://arxiv.org/abs/alg-geom/9302003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149797
dc.subjectAlgebraic Geometry
dc.titleLefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes
dc.typetext

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