A vanishing theorem for log canonical pairs

TL;DR

This paper establishes a vanishing theorem for log canonical pairs using inversion of adjunction, generalizing bounds on Castelnuovo--Mumford regularity to broader classes of projective schemes.

Contribution

It introduces a new vanishing property for ideals on projective varieties, extending previous results to schemes with log canonical singularities.

Findings

Generalized Castelnuovo--Mumford regularity bounds

Recovered known results as special cases

Validated results through multiple examples

Abstract

Using inversion of adjunction, we deduce from Nadel's theorem a vanishing property for ideals sheaves on projective varieties, a special case of which recovers a result due to Bertram--Ein--Lazarsfeld. This enables us to generalize to a large class of projective schemes certain bounds on Castelnuovo--Mumford regularity previously obtained by Bertram--Ein--Lazarsfeld in the smooth case and by Chardin--Ulrich for locally complete intersection varieties with rational singularities. Our results are tested on several examples.