Betti tables of monomial ideals fixed by permutations of the variables

Satoshi Murai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let Sn be a polynomial ring with n variables over a field and {In}n≥1 a chain of ideals such that each In is a monomial ideal of Sn fixed by permutations of the variables. In this paper, we present a way to determine all nonzero positions of Betti tables of In for all large intergers n from the Zmgraded Betti tables of Im for some small integers m. Our main result shows that the projective dimension and the regularity of In eventually become linear functions on n, confirming a special case of conjectures posed by Le, Nagel, Nguyen and Römer.

Original languageEnglish
Pages (from-to)7087-7107
Number of pages21
JournalTransactions of the American Mathematical Society
Volume373
Issue number10
DOIs
Publication statusPublished - 2020 Oct

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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