Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes
| dc.creator | Sardo-Infirri, Sacha | |
| dc.date | 1993-02-09 | |
| dc.date.accessioned | 2026-07-07T09:05:48Z | |
| dc.date.available | 2026-07-07T09:05:48Z | |
| dc.description | 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}. | |
| dc.description | 29 pages, latex 2.09 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9302003 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9302003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149797 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes | |
| dc.type | text |