Normal Rees algebras arising from vertex decomposable simplicial complexes

2023/11/25 by Somayeh Moradi, Moradi, Somayeh · 1 citation
Computer Science · Mathematics · #13A30 #13F55 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2311.15135

openalex publication_date 2023/11/25 · openalex created_date 2023/11/29 · openalex updated_date 2026/07/28

Abstract

We show that for a vertex decomposable simplicial complex Δ, the Rees algebra of I_Δ^\vee is a normal Cohen-Macaulay domain. As consequences, we show that any squarefree weakly polymatroidal ideal is normal and we obtain normal ideals among several interesting families of monomial ideals such as cover ideals of graphs and edge ideals of hypergraphs. Moreover, based on a construction on simplicial complexes given by Biermann and Van Tuyl [2], we present families of normal ideals attached to any squarefree monomial ideal.

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