Toric rings arising from cyclic polytopes
Takayuki Hibi, Akihiro Higashitani, Lukas Katth"an, Ryota Okazaki
TL;DR
This paper investigates the algebraic properties of toric rings derived from integral cyclic polytopes, focusing on Cohen-Macaulayness, Gorenstein conditions, and normality, providing complete characterizations and conditions.
Contribution
It offers a complete characterization of when these toric rings are Gorenstein and discusses Serre's condition for Cohen-Macaulayness, also analyzing normality of related semigroup rings.
Findings
Characterization of Gorenstein toric rings from cyclic polytopes
Conditions for Cohen-Macaulayness based on Serre's condition
Normality criteria for semigroup rings generated by vertices
Abstract
In the present paper, we consider the problem when the toric ring arising from an integral cyclic polytope is Cohen-Macaulay by discussing Serre's condition and we give a complete characterization when that is Gorenstein. Moreover, we study the normality of the other semigroup ring arising from an integral cyclic polytope but generated only with its vertices.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models