New York Journal of Mathematics
Volume 22 (2016) 1487-1502

  

Wee Liang Gan

A long exact sequence for homology of FI-modules

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Published: December 9, 2016
Keywords: FI-module, Castelnuovo-Mumford regularity, homological degree
Subject: 18G15

Abstract
We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FI-module which is generated and related in finite degree, if it has a nonzero higher homology, then its homological degrees are strictly increasing (starting from the first homological degree).

Author information

Department of Mathematics, University of California, Riverside, CA 92521, USA
wlgan@math.ucr.edu