Local cohomology and the multi-graded regularity of FI$^m$-modules

Liping Li; Eric Ramos

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arXiv · 1711.07964

Local cohomology and the multi-graded regularity of FI$^m$-modules

Liping Li·Eric Ramos

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Abstract

We develop a local cohomology theory for FI$^m$-modules, and show that it in many ways mimics the classical theory for multi-graded modules over a polynomial ring. In particular, we define an invariant of FI$^m$-modules using this local cohomology theory which closely resembles an invariant of multi-graded modules over Cox rings defined by Maclagan and Smith. It is then shown that this invariant behaves almost identically to the invariant of Maclagan and Smith.

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BibTeX RIS

Liping Li, Eric Ramos. 2017-11-21. Local cohomology and the multi-graded regularity of FI$^m$-modules. https://arxiv.org/abs/1711.07964

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