Betti numbers of symmetric shifted ideals

Jennifer Biermann, Hernán de Alba, Federico Galetto, Satoshi Murai, Uwe Nagel, Augustine O'Keefe, Tim Römer, Alexandra Seceleanu

Research output: Contribution to journalArticle

Abstract

We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetric shifted ideal has linear quotients and compute its (equivariant) graded Betti numbers. As an application of this result, we obtain several consequences for graded Betti numbers of symbolic powers of defining ideals of star configurations.

Original languageEnglish
Pages (from-to)312-342
Number of pages31
JournalJournal of Algebra
Volume560
DOIs
Publication statusPublished - 2020 Oct 15

Keywords

  • Betti numbers
  • Equivariant resolution
  • Linear quotients
  • Shifted ideal
  • Star configuration
  • Symbolic power

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Biermann, J., de Alba, H., Galetto, F., Murai, S., Nagel, U., O'Keefe, A., Römer, T., & Seceleanu, A. (2020). Betti numbers of symmetric shifted ideals. Journal of Algebra, 560, 312-342. https://doi.org/10.1016/j.jalgebra.2020.04.037