Asymptotic behaviour of castelnuovo-mumford regularity

Kodiyalam, Vijay (2000) Asymptotic behaviour of castelnuovo-mumford regularity Proceedings of the American Mathematical Society, 128 (02). pp. 407-412. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2000-128-02/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9939-99-05020-0

Abstract

Let S be a polynomial ring over a field. For a graded S-module generated in degree at most P, the Castelnuovo-Mumford regularity of each of (i) its nth symmetric power, (ii) its nth torsion-free symmetric power and (iii) the integral closure of its nth torsion-free symmetric power is bounded above by a linear function in n with leading coefficient at most P. For a graded ideal I of S, the regularity of In is given by a linear function of n for all sufficiently large n. The leading coefficient of this function is identified.

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