Castelnuovo-Mumford regularity by approximation
Commutative Algebra
2012-01-25 v2 Algebraic Geometry
Combinatorics
Abstract
The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups.
Cite
@article{arxiv.math/0211279,
title = {Castelnuovo-Mumford regularity by approximation},
author = {Harm Derksen and Jessica Sidman},
journal= {arXiv preprint arXiv:math/0211279},
year = {2012}
}
Comments
Sections 2 and 3 revised to incorporate changes in definitions and terminology.Typos corrected and references updated. 20 pages, AMS LaTex