Castelnuovo-Mumford regularity of products of ideals

Details Castelnuovo-Mumford regularity of products of ideals Castelnuovo-Mumford regularity of products of ideals

2002-10-04

arxiv.org/abs/math/0210065v1

Mathematics

Commutative Algebra

14 pages

Scientific paper

We discuss the behavior of the Castelnuovo-Mumford regularity under certain operations on ideals and modules, like products or powers. In particular, we show that reg(IM) can be larger than reg(M)+reg(I) even when I is an ideal of linear forms and M is a module with a linear resolution. On the other hand, we show that any product of ideals of linear forms has a linear resolution. We also discuss the case of polymatroidal ideals and show that any product of determinantal ideals of a generic Hankel matrix has a linear resolution.

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