2009/04/12 by Victor V. Batyrev, Victor Batyrev, Batyrev, Victor +2
Mathematics · #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #math.CO #msc:14M25
paper · pdf · doi:10.48550/arxiv.0904.1880
Dedicated to the memory of Professor V. A Iskovskih, 34 pages, LaTeX
arxiv created 2009/04/12 · openalex publication_date 2009/04/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A n-dimensional Gorenstein toric Fano variety X is called Del Pezzo variety if the anticanonical class -KX is a (n-1)-multiple of a Cartier divisor. Our purpose is to give a complete biregular classfication of Gorenstein toric Del Pezzo varieties in arbitrary dimension n ≥ 2. We show that up to isomorphism there exist exactly 37 Gorenstein toric Del Pezzo varieties of dimension n which are not cones over (n-1)-dimensional Gorenstein toric Del Pezzo varieties. Our results are closely related to the classification of all Minkowski sum decompositions of reflexive polygons due to Emiris and Tsigaridas and to the classification up to deformation of n-dimensional almost Del Pezzo manifolds obtained by Jahnke and Peternell.