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 journalArticlepeer-review

13 Scopus citations

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
StatePublished - Oct 15 2020

Bibliographical note

Funding Information:
The research of the fourth author is partially supported by KAKENHI 16K05102 . The fifth author was partially supported by Simons Foundation grant # 317096 . The last author was supported by NSF grant DMS–1601024 and EPSCoR award OIA–1557417 .

Funding Information:
The research of the fourth author is partially supported by KAKENHI 16K05102. The fifth author was partially supported by Simons Foundation grant #317096. The last author was supported by NSF grant DMS?1601024 and EPSCoR award OIA?1557417.

Publisher Copyright:
© 2020 Elsevier Inc.

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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