Castelnuovo--Mumford Regularity and Log-canonical Thresholds

TL;DR

This paper establishes a precise inequality linking the Castelnuovo--Mumford regularity of an ideal sheaf with its log-canonical threshold, advancing understanding in algebraic geometry.

Contribution

It introduces a new sharp inequality connecting regularity and log-canonical thresholds, providing a novel theoretical insight.

Findings

Proved a sharp inequality between regularity and log-canonical threshold.

Enhanced understanding of the relationship between algebraic invariants.

Potential applications in algebraic geometry and singularity theory.

Abstract

We prove a sharp inequality relating the Castelnuovo--Mumford regularity of a coherent ideal sheaf to its log-canonical threshold.