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arXiv · 1609.06396

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

Federico Galetto
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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. 2016-09-21. On the ideal generated by all squarefree monomials of a given degree. https://doi.org/10.1216/jca.2020.12.199

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