Initially regular sequences and depths of ideals

2018/10/02 by Fouli, Louiza, Ha, Huy Tai, Morey, Susan
#05E40 #13C15 #13D05 #13F20 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.01512

Abstract

For an arbitrary ideal I in a polynomial ring R we define the notion of initially regular sequences on R/I. These sequences share properties with regular sequences. In particular, the length of an initially regular sequence provides a lower bound for the depth of R/I. Using combinatorial information from the initial ideal of I we construct sequences of linear polynomials that form initially regular sequences on R/I. We identify situations where initially regular sequences are also regular sequences, and we show that our results can be combined with polarization to improve known depth bounds for general monomial ideals.

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