Remarks on the Hilbert depth of squarefree monomial ideals

2023/10/18 by Balanescu, Silviu, Cimpoeas, Mircea
Computer Science · Mathematics · #05A18 #06A07 #13C15 #13F20 #13P10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2310.12339

openalex publication_date 2023/10/18 · openalex created_date 2023/10/21 · openalex updated_date 2026/07/28

Abstract

Let K be a infinite field, S=K[x₁,…,x_n] and 0⊂ I\subsetneq J⊂ S two squarefree monomial ideals. In a previous paper we proved a new formula for the Hilbert depth of J/I. In this paper, we illustrate how one can use the Stanley-Reisner correspondence between (relative) simplicial complexes and (quotients of) squarefree monomial ideals, in order to reobtain some basic properties of the Hilbert depth. More precisely, we show that depth(J/I)≤ hdepth(J/I)≤ dim(J/I). Also, we show that hdepth(I)≥ hdepth(S/I)+1, if S/I is Cohen-Macaulay.

Related

• On the Hilbert depth of monomial ideals
• On the Hilbert depth of a special class of squarefree monomial ideals
• Comparing Hilbert depth of I with Hilbert depth of S/I. II
• Comparing Hilbert depth of I with Hilbert depth of S/I
• Comparing Hilbert depth of I with Hilbert depth of S/I. III