On smooth lattice polytopes with small degree

Carolina Araujo; Douglas Monsôres

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arXiv · 1302.1413

On smooth lattice polytopes with small degree

Carolina Araujo·Douglas Monsôres

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Abstract

Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this paper we explore this correspondence to classify smooth lattice polytopes having small degree, extending a classification provided by Dickenstein, Di Rocco and Piene. Our approach consists in interpreting the degree of a polytope as a geometric invariant of the corresponding polarized variety, and then applying techniques from Adjunction Theory and Mori Theory.

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Carolina Araujo, Douglas Monsôres. 2013-02-07. On smooth lattice polytopes with small degree. https://arxiv.org/abs/1302.1413

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