Kawamata-Viehweg vanishing for toric varieties

TL;DR

This paper proves the Kawamata-Viehweg vanishing theorem for klt pairs on projective toric varieties, extending the understanding of vanishing theorems in algebraic geometry.

Contribution

It establishes the Kawamata-Viehweg vanishing theorem specifically for klt pairs on projective toric varieties, a case not previously confirmed.

Findings

Kawamata-Viehweg vanishing holds for klt pairs on projective toric varieties

Extension of vanishing theorems to new classes of algebraic varieties

Enhanced understanding of the geometry of toric varieties

Abstract

Given a boundary divisor $B$ on a projective toric variety $X$ such that $(X, B)$ is klt, we establish the Kawamata-Viehweg vanishing theorem for $(X, B)$.