On the behavior of Castelnuovo-Mumford regularity with respect to some functors

Abstract

We investigate the behavior of Castelnuovo-Mumford regularity with respect to some classical functors : Tor, the Frobenius functor in positive characteristic, taking a power or a product (on ideals). These generalizes and refines previous results on these issues by several authors. As an application we provide results on the regularity of an intersection of subschemes of a projective scheme, under appropriate geometric hypotheses. Results on the rigidity of multiple Tor modules and on the characterization of their vanishing are given, motivated by geometric applications.

References in corpus (2)

• Castelnuovo-Mumford regularity of products of ideals
• On the regularity over positively graded algebras

Cited by in corpus (9)

• Resurgences for ideals of special point configurations in ${\mathbf{P}}^N$ coming from hyperplane arrangements
• On the regularity over positively graded algebras
• A note on the growth of regularity with respect to Frobenius
• The Initial Degree of Symbolic Powers of Fermat-like Ideals of Planes and Lines Arrangements
• Implicitization of de Jonquières parametrizations
• Generalized local cohomology and regularity of Ext modules
• Koszul determinantal rings and $2\times e$ matrices of linear forms
• The (ir)regularity of Tor and Ext
• Castelnuovo-Mumford regularity and the discreteness of $F$-jumping coefficients in graded rings