Regular Sequences On Squares Of Monomial Ideals

2021/12/23 by Fouli, Louiza, Hà, Tài Huy, Morey, Susan
#05E40 #13C15 #13D05 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.12305

Abstract

We use initially regular sequences that consist of linear sums to explore the depth of R/I², when I is a monomial ideal in a polynomial ring R. We give conditions under which these linear sums form regular or initially regular sequences on R/I². We then obtain a criterion for when \depth R/I²>1 and a lower bound on \depth R/I².

Related

• Initially regular sequences and depths of ideals
• Remarks on the Stanley depth and Hilbert depth of monomial ideals with linear quotients
• Upper bounds of depth of monomial ideals
• On the Hilbert depth of monomial ideals
• Combinatorial Reductions for the Stanley Depth of I and S/I