Torsionfreeness for divisor class groups of toric rings of integral polytopes

2022/02/22 by Koji Matsushita, Matsushita, Koji
Mathematics · #52B20 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Primary 13F65 #Secondary 13C20 #math.AC #math.CO #msc:13C20 #msc:13F65 #msc:52B20

paper · pdf · doi:10.48550/arxiv.2202.10686

8 pages, 3 figures

arxiv created 2022/02/22 · openalex publication_date 2022/02/22 · arxiv updated 2022/02/23 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In the present paper, we give some sufficient conditions for Cl(\Bbbk[P]) to be torsionfree, where Cl(\Bbbk[P]) denote the divisor class group of the toric ring \Bbbk[P] of an integral polytope P. We prove that Cl(\Bbbk[P]) is torsionfree if P is compressed, and Cl(\Bbbk[P]) is torsionfree if P is a (0,1)-polytope which has at most dim P+2 facets. Moreover, we characterize the toric rings of (0,1)-polytopes in the case Cl(\Bbbk[P])≅ ℤ.

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