2000/01/19 by Alexandr Borisov, Borisov, Alexandr · 2 citations
Mathematics · #14B05 #14E30 #14M25 #52B20 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14B05 #msc:14E30 #msc:14M25 #msc:52B20
paper · pdf · doi:10.48550/arxiv.math/0001109
13 pages, 43 references
arxiv created 2000/01/19 · openalex publication_date 2000/01/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is pretty well-known that toric Fano varieties of dimension k with terminal singularities correspond to convex lattice polytopes P in Rk of positive finite volume, such that intersection of P and Zk consists of the point 0 and vertices of P. Likewise, Q-factorial terminal toric singularities essentially correspond to lattice simplexes with no lattice points inside or on the boundary (except the vertices). There have been a lot work, especially in the last 20 years or so on classification of these objects. The main goal of this paper is to bring together these and related results, that are currently scattered in the literature. We also want to emphasize the deep similarity between the problems of classification of toric Fano varieties and classification of Q-factorial toric singularities.