Vanishing Theorems on Toric Varieties, with Erratum to a Former Paper

TL;DR

This paper corrects previous errors and employs positive characteristic methods to reprove key vanishing theorems and spectral sequence degeneration results for toric varieties over arbitrary fields.

Contribution

It clarifies past mistakes and provides new proofs of important vanishing theorems on toric varieties using positive characteristic techniques.

Findings

Corrected previous inaccuracies in vanishing theorems

Reproved Bott vanishing theorem in positive characteristic

Established degeneration of Hodge to de Rham spectral sequence

Abstract

In this paper, we clarify the mistakes made in the former article entitled "Vanishing Theorems on Toric Varieties in Positive Characteristic". On the other hand, we use the positive characteristic method to reprove the Bott vanishing theorem, the degeneration of the Hodge to de Rham spectral sequence and the Kawamata-Viehweg vanishing theorem for log pairs on toric varieties over a field of arbitrary characteristic, where concerned Weil divisors are torus invariant.