Nonvanishing for threefolds in characteristic $p>5$

TL;DR

This paper proves a key algebraic geometry theorem called the Nonvanishing Theorem for three-dimensional varieties over algebraically closed fields with characteristic greater than five.

Contribution

It establishes the Nonvanishing Theorem for threefolds specifically in characteristic p > 5, extending previous results to positive characteristic.

Findings

Nonvanishing Theorem proven for threefolds in characteristic p > 5

Advances understanding of algebraic geometry in positive characteristic

Supports further research in minimal model program in characteristic p

Abstract

We prove the Nonvanishing Theorem for threefolds over an algebraically closed field $k$ of characteristic $p >5$.