Alexander duality for the alternative polarizations of strongly stable ideals

Kosuke Shibata, Kohji Yanagawa

Research output: Contribution to journalArticlepeer-review

Abstract

We will define the Alexander duality for strongly stable ideals. More precisely, for a strongly stable ideal (Formula presented.) with (Formula presented.) for all (Formula presented.) its dual (Formula presented.) is a strongly stable ideal with (Formula presented.) for all (Formula presented.) This duality has been constructed by Fløystad et al.in a different manner, so we emphasis applications here. For example, we will describe the Hilbert series of the local cohomologies (Formula presented.) using the irreducible decomposition of I (through the Betti numbers of (Formula presented.)).

Original languageEnglish
Pages (from-to)3011-3030
Number of pages20
JournalCommunications in Algebra
Volume48
Issue number7
DOIs
Publication statusPublished - Jul 2 2020

Keywords

  • Alexander duality
  • alternative polarizations
  • irreducible decomposition (of a monomial ideal)
  • local cohomology
  • strongly stable ideals

ASJC Scopus subject areas

  • Algebra and Number Theory

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