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

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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Cited by in corpus (4)

• Betti numbers of symmetric shifted ideals
• An equivariant Hochster's formula for ${\mathfrak{S}}_n$-invariant monomial ideals
• Setting the scene for Betti characters
• Characteristic Independence of Betti Numbers of Monomial Ideals in Five Variables