On the ideal generated by all squarefree monomials of a given degree

Federico Galetto

doi:10.1216/jca.2020.12.199

Abstract

An explicit construction is given of a minimal free resolution of the ideal generated by all squarefree monomials of a given degree. The construction relies upon and exhibits the natural action of the symmetric group on the syzygy modules. The resolution is obtained over an arbitrary coefficient ring; in particular, it is characteristic free. Two applications are given: an equivariant resolution of De Concini–Procesi rings indexed by hook partitions, and a resolution of FI-modules.

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Federico Galetto. "On the ideal generated by all squarefree monomials of a given degree." J. Commut. Algebra 12 (2) 199 - 215, Summer 2020. https://doi.org/10.1216/jca.2020.12.199

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Received: 15 February 2017; Revised: 24 October 2017; Accepted: 28 October 2017; Published: Summer 2020

First available in Project Euclid: 2 June 2020

zbMATH: 07211335

MathSciNet: MR4105544

Digital Object Identifier: 10.1216/jca.2020.12.199

Subjects:

Primary: 13D02

Secondary: 13A50

Keywords: characteristic-free , De Concini–Procesi , equivariant resolution , FI-module , squarefree monomial ideal

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