# On the base point free theorem for klt threefolds in large characteristic

## TL;DR

This paper refines the base point free theorem for Kawamata log terminal threefolds over large characteristic fields, establishing conditions under which certain linear systems are base point free.

## Contribution

It provides a new criterion for base point freeness of divisors on klt threefolds in large characteristic, extending previous results in positive characteristic.

## Key findings

- Linear system |mL| is base point free for large m under given conditions.
- Refinement of the base point free theorem for threefolds in characteristic p >> 0.
- Conditions involving nef divisors and big nef differences are sufficient for base point freeness.

## Abstract

In this article we present a refinement of the base point free theorem for threefolds in positive characteristic. If $L$ is a nef Cartier divisor of numerical dimension at least one on a projective Kawamata log terminal threefold $(X,\Delta)$ over a perfect field $k$ of characteristic $p \gg 0$ such that $L-(K_X+\Delta)$ is big and nef, then we show that the linear system $|mL|$ is base point free for all sufficiently large integer $m>0$.