A COLORFUL HOCHSTER FORMULA AND UNIVERSAL PARAMETERS FOR FACE RINGS

Ashleigh Adams, Victor Reiner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper has two related parts. The first generalizes Hochster’s formula on resolutions of Stanley– Reisner rings to a colorful version, applicable to any proper vertex-coloring of a simplicial complex. The second part examines a universal system of parameters for Stanley–Reisner rings of simplicial complexes, and more generally, face rings of simplicial posets. These parameters have good properties, including being fixed under symmetries, and detecting depth of the face ring. Moreover, when resolving the face ring over these parameters, the shape is predicted, conjecturally, by the colorful Hochster formula.

Original languageEnglish (US)
Pages (from-to)151-176
Number of pages26
JournalJournal of Commutative Algebra
Volume15
Issue number2
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© Rocky Mountain Mathematics Consortium

Keywords

  • Hochster formula
  • Stanley–Reisner
  • balanced
  • depth
  • simplicial poset
  • symmetry

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