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

Authors :: Federico Galetto
Source :: J. Commut. Algebra 12, no. 2 (2020), 199-215
Publication Year :: 2020
Publisher :: Rocky Mountain Mathematics Consortium, 2020.
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.<br />Comment: Updated references

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