Castelnuovo-Mumford regularity of associated graded modules and fiber cones of filtered modules

TL;DR

This paper establishes bounds on the Castelnuovo-Mumford regularity for associated graded modules and fiber cones of filtered modules, extending previous theoretical results in algebraic geometry and commutative algebra.

Contribution

It provides new bounds on regularity for associated graded modules and fiber cones, generalizing earlier work by Rossi-Trung-Valla and Linh.

Findings

Bounds on regularity for associated graded modules

Bounds on regularity for fiber cones

Extension of previous theoretical results

Abstract

We give bounds on the Castelnuovo-Mumford regularity of the associated graded module of an arbitrary good filtration and of its fiber cone. These bounds extend previous results of Rossi-Trung-Valla and Linh.