Conic divisorial ideals of toric rings and applications to Hibi rings and stable set rings

2022/10/05 by Koji Matsushita, Matsushita, Koji · 2 citations
Mathematics · #05C25 #14M25 #16S38 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13C14 #Representation Theory (math.RT) #Rings, Modules, and Algebras #Secondary 13F65

paper · pdf · doi:10.48550/arxiv.2210.02031

openalex publication_date 2022/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we study conic divisorial ideals of toric rings. We provide an idea to determine them and we give a description of the conic divisorial ideals of Hibi rings and stable set rings of perfect graphs by using this idea. We also characterize when Hibi rings or stable set rings are quasi-symmetric or weakly-symmetric. Moreover, by using the description of the conic divisorial ideals, we construct a non-commutative crepant resolution (NCCR) of a special family of stable set rings.

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• Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
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