Codimension and projective dimension up to symmetry

Dinh Van Le, Uwe Nagel, Hop D. Nguyen, Tim Römer

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are investigated. We focus on the asymptotic behavior of codimensions and projective dimensions of ideals in such a chain. If the ideals are graded it is known that the codimensions grow eventually linearly. Here this result is extended to chains of arbitrary symmetric ideals. Moreover, the slope of the linear function is explicitly determined. We conjecture that the projective dimensions also grow eventually linearly. As part of the evidence we establish two non-trivial lower linear bounds of the projective dimensions for chains of monomial ideals. As an application, this yields Cohen–Macaulayness obstructions.

Original languageEnglish
Pages (from-to)346-362
Number of pages17
JournalMathematische Nachrichten
Volume293
Issue number2
DOIs
StatePublished - Feb 1 2020

Bibliographical note

Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Keywords

  • 13A50
  • 13C15
  • 13D02
  • 13F20
  • 16P70
  • 16W22
  • invariant ideal
  • monoid
  • polynomial ring
  • symmetric group

ASJC Scopus subject areas

  • General Mathematics

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