Initially regular sequences and depths of ideals

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 when I is homogeneous. Using com...

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Bibliographic Details
Published inJournal of algebra Vol. 559; pp. 33 - 57
Main Authors Fouli, Louiza, Hà, Huy Tài, Morey, Susan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2020
Subjects
Depth
Edge ideal
Gröbner basis
Initial ideal
Monomial ideal
Projective dimension
Regular sequence
Monomial ideal
05E40
Regular sequence
Edge ideal
Gröbner basis
Initial ideal
Projective dimension
13P10
13F20
13D05
Depth
13C15
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Summary: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 when I is homogeneous. 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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.03.027