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arXiv · 1802.06735

When are permutation invariants Cohen-Macaulay over all fields?

Ben Blum-Smith·Sophie Marques
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Abstract

We prove that the polynomial invariants of a permutation group are Cohen-Macaulay for any choice of coefficient field if and only if the group is generated by transpositions, double transpositions, and 3-cycles. This unites and generalizes several previously known results. The "if" direction of the argument uses Stanley-Reisner theory and a recent result of Christian Lange in orbifold theory. The "only-if" direction uses a local-global result based on a theorem of Raynaud to reduce the problem to an analysis of inertia groups, and a combinatorial argument to identify inertia groups that obstruct Cohen-Macaulayness.

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Ben Blum-Smith, Sophie Marques. 2018-05-17. When are permutation invariants Cohen-Macaulay over all fields?. https://doi.org/10.2140/ant.2018.12.1787

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