A Bound for the Castelnuovo-Mumford Regularity of Log Canonical Varieties

TL;DR

This paper establishes an upper bound on the Castelnuovo-Mumford regularity for ideals defining varieties with log canonical singularities, linking algebraic complexity to generator degrees.

Contribution

It provides a new bound for regularity specifically for ideals with log canonical singularities, extending previous results to this class.

Findings

Bound for regularity in terms of generator degrees

Applicable to ideals defining local complete intersections with log canonical singularities

Advances understanding of algebraic complexity in singular varieties

Abstract

In this note, we give a bound for the Castelnuovo-Mumford regularity of a homogeneous ideal $I$ in terms of the degrees of its generators. We assume that $I$ defines a local complete intersection with log canonical singularities.