Effective freeness and very ampleness in positive characteristic

TL;DR

This paper proves a basepoint free theorem and provides effective bounds for very ampleness in algebraic geometry over fields of positive characteristic, advancing understanding of line bundle properties in this setting.

Contribution

It introduces a positive characteristic analogue of the Angehrn-Siu basepoint free theorem and offers explicit bounds for very ampleness, filling gaps in existing theory.

Findings

Established a basepoint free theorem in positive characteristic.

Provided effective bounds for very ampleness in arbitrary characteristic.

Extended classical results to new algebraic geometric contexts.

Abstract

In this paper, we establish a basepoint free theorem of Angehrn-Siu type in positive characteristic. Moreover, we also give an effective bound for very ampleness in arbitrary characteristic.