Castelnuovo-Mumford regularity of products of ideals

Abstract

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.

14 pages

Cited by in corpus (23)

• On the behavior of Castelnuovo-Mumford regularity with respect to some functors
• Pretty clean monomial ideals and linear quotients
• Persistence and stability properties of powers of ideals
• Stanley decompositions and partitionable simplicial complexes
• Gotzmann lexsegment ideals
• Symmetric and Quasi-Symmetric Functions associated to Polymatroids
• Monomial ideals with linear quotients and componentwise (support-)linearity
• Cohen-Macaulay Polymatroidal Ideals
• Generalized local cohomology and regularity of Ext modules
• Some families of componentwise linear monomial ideals
• Castelnuovo-Mumford regularity and Gorensteinness of fiber cone
• Powers of Principal $Q$-Borel ideals
• Ideals generated by $a$-fold products of linear forms have linear graded free resolution
• Some arithmetic properties of matroidal ideals
• On the minimal graded free resolution of powers of lexsegment ideals
• The depth of powers of an ideal
• On certain equidimensional polymatroidal ideals
• $k$-shellable simplicial complexes and graphs
• Degree bounds for invariant skew polynomials
• Products of polymatroids with the strong exchange property
• Contribution in combinatorics in commutative algebra.(ph-d thesis)
• Integrally closed and componentwise linear ideals
• Linearization of monomial ideals