An Enriques Classification Theorem for Surfaces in Positive Characteristic

TL;DR

This paper establishes a classification theorem for certain algebraic surfaces in positive characteristic, showing they are birational to abelian surfaces under specific conditions.

Contribution

It provides a new Enriques classification theorem for smooth projective surfaces over fields with characteristic greater than 3, under particular numerical conditions.

Findings

Surfaces with specified invariants are birational to abelian surfaces.

The theorem applies to surfaces over algebraically closed fields of characteristic p>3.

It advances understanding of surface classification in positive characteristic.

Abstract

We prove that a smooth projective surface $S$ over an algebraically closed field of characteristic $p>3$ is birational to an abelian surface if $P_1(S)=P_4(S)=1$ and $h^1(S,\mathcal{O}_S)=2$.