Summer 2023 A COLORFUL HOCHSTER FORMULA AND UNIVERSAL PARAMETERS FOR FACE RINGS
Ashleigh Adams, Victor Reiner
J. Commut. Algebra 15(2): 151-176 (Summer 2023). DOI: 10.1216/jca.2023.15.151

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.

Citation

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Ashleigh Adams. Victor Reiner. "A COLORFUL HOCHSTER FORMULA AND UNIVERSAL PARAMETERS FOR FACE RINGS." J. Commut. Algebra 15 (2) 151 - 176, Summer 2023. https://doi.org/10.1216/jca.2023.15.151

Information

Received: 27 January 2021; Accepted: 28 January 2021; Published: Summer 2023
First available in Project Euclid: 29 June 2023

MathSciNet: MR4611107
zbMATH: 07725182
Digital Object Identifier: 10.1216/jca.2023.15.151

Subjects:
Primary: 13F50 , 13F55
Secondary: 13D02

Keywords: balanced , depth , Hochster formula , simplicial poset , Stanley–Reisner , symmetry

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

Vol.15 • No. 2 • Summer 2023
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