On smooth lattice polytopes with small degree

2013/02/06 by Carolina Araujo, Araujo, Carolina, Douglas Monsôres +1
Mathematics · #14E30 #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E30 #msc:14M25

paper · pdf · doi:10.48550/arxiv.1302.1413

12 pages. v2: attributions fixed, reference added

arxiv created 2013/02/07 · arxiv updated 2013/02/08

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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