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

2017/11/21 by Li, Liping, Ramos, Eric
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1711.07964

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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