On Steenbrink vanishing for rational singularities in positive characteristic

TL;DR

This paper proves a special case of Steenbrink vanishing for rational singularities in positive characteristic, demonstrating that certain threefolds satisfy this vanishing under specific conditions.

Contribution

It establishes Steenbrink vanishing for rational singularities in positive characteristic and applies it to strongly F-regular and klt threefolds in characteristic p>41.

Findings

Steenbrink vanishing holds for rational singularities in positive characteristic in a special case.

Strongly F-regular threefolds in characteristic p>41 satisfy Steenbrink vanishing.

Klt threefolds in characteristic p>41 also satisfy Steenbrink vanishing.

Abstract

We show a special case of Steenbrink vanishing for rational singularities in positive characteristic. As a consequence, we prove that strongly $F$-regular threefolds and klt threefolds in characteristic $p>41$ satisfy Steenbrink vanishing.