Depth in a pathological case

2014/06/05 by Dorin Popescu, Popescu, Dorin
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1406.1398

openalex publication_date 2014/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be a squarefree monomial ideal of a polynomial algebra over a field minimally generated by f₁,...,f_r of degree d≥ 1, and a set E of monomials of degree ≥ d+1. Let J\subsetneq I be a squarefree monomial ideal generated in degree ≥ d+1. Suppose that all squarefree monomials of I∖ (J∪ E) of degree d+1 are some least common multiples of f_i. If J contains all least common multiples of two of (f_i) of degree d+2 then \depth_SI/J≤ d+1 and Stanley's Conjecture holds for I/J.

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