On base point free theorem and Mori dream spaces for log canonical threefolds over the algebraic closure of a finite field

TL;DR

This paper extends the base point free theorem to log canonical threefolds over algebraically closed finite fields without the bigness condition in characteristic greater than five and explores Mori dream spaces in this setting.

Contribution

It removes the bigness restriction for the base point free theorem on threefolds over finite fields in characteristic >5 and investigates properties of Mori dream spaces over such fields.

Findings

Base point free theorem holds without bigness condition in characteristic >5.

Mori dream spaces are characterized over algebraically closed finite fields.

Extension of known results to more general threefolds in positive characteristic.

Abstract

The authors and D. Martinelli proved the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field. In this paper, we drop the bigness condition when the characteristic is larger than five. Additionally, we discuss Mori dream spaces defined over the algebraic closure of a finite field.