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On the ideal generated by all squarefree monomials of a given degree. (English) Zbl 1442.13037

Summary: 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.

MSC:

13D02 Syzygies, resolutions, complexes and commutative rings
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
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References:

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