Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs

TL;DR

This paper extends the Kodaira vanishing theorem to log-canonical and semi-log-canonical pairs, providing new vanishing results that are important in algebraic geometry.

Contribution

It proves the Kodaira vanishing theorem for these pairs and introduces a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.

Findings

Kodaira vanishing theorem proven for log-canonical pairs

Relative vanishing theorem of Reid--Fukuda type established

Enhances understanding of vanishing theorems in singular algebraic geometry

Abstract

We prove the Kodaira vanishing theorem for log-canonical and semi-log-canonical pairs. We also give a relative vanishing theorem of Reid--Fukuda type for semi-log-canonical pairs.