# Castelnuovo-Mumford regularity of products of ideals.

Collectanea Mathematica (2003)

• Volume: 54, Issue: 2, page 137-152
• ISSN: 0010-0757

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## Abstract

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The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask, for instance, wether the Castelnuovo-Mumford regularity reg(IM) of the product of an ideal I with a module M is bouded by the sum reg(I) + reg(M). In general this is not the case. But we show that it is indeed the case if either dim R/I ≤ 1 or I is generic (in a very precise sense). Further we show that products of ideals of linear forms have always a linear resolution and that the same is true for products of determinantal ideals of a generic Hankel matrix.

## How to cite

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Conca, Aldo, and Herzog, Jürgen. "Castelnuovo-Mumford regularity of products of ideals.." Collectanea Mathematica 54.2 (2003): 137-152. <http://eudml.org/doc/43058>.

@article{Conca2003,
abstract = {The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask, for instance, wether the Castelnuovo-Mumford regularity reg(IM) of the product of an ideal I with a module M is bouded by the sum reg(I) + reg(M). In general this is not the case. But we show that it is indeed the case if either dim R/I ≤ 1 or I is generic (in a very precise sense). Further we show that products of ideals of linear forms have always a linear resolution and that the same is true for products of determinantal ideals of a generic Hankel matrix.},
author = {Conca, Aldo, Herzog, Jürgen},
journal = {Collectanea Mathematica},
keywords = {Regularidad; Ideal de operadores; Castelnuovo-Mumford regularity; linear resolutions; ideals of linear forms},
language = {eng},
number = {2},
pages = {137-152},
title = {Castelnuovo-Mumford regularity of products of ideals.},
url = {http://eudml.org/doc/43058},
volume = {54},
year = {2003},
}

TY - JOUR
AU - Conca, Aldo
AU - Herzog, Jürgen
TI - Castelnuovo-Mumford regularity of products of ideals.
JO - Collectanea Mathematica
PY - 2003
VL - 54
IS - 2
SP - 137
EP - 152
AB - The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask, for instance, wether the Castelnuovo-Mumford regularity reg(IM) of the product of an ideal I with a module M is bouded by the sum reg(I) + reg(M). In general this is not the case. But we show that it is indeed the case if either dim R/I ≤ 1 or I is generic (in a very precise sense). Further we show that products of ideals of linear forms have always a linear resolution and that the same is true for products of determinantal ideals of a generic Hankel matrix.
LA - eng
KW - Regularidad; Ideal de operadores; Castelnuovo-Mumford regularity; linear resolutions; ideals of linear forms
UR - http://eudml.org/doc/43058
ER -

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