Fujita's conjecture for quasi-elliptic surfaces

TL;DR

This paper proves Fujita's conjecture for quasi-elliptic surfaces, establishing conditions under which certain line bundles are base point free or very ample, thus advancing understanding in algebraic geometry.

Contribution

It confirms Fujita's conjecture specifically for quasi-elliptic surfaces, providing explicit bounds for base point freeness and very ampleness.

Findings

$K_X + tA$ is base point free for $t \,\geq\, 3$

$K_X + tA$ is very ample for $t \,\geq\, 4$

Fujita's conjecture holds for quasi-elliptic surfaces

Abstract

We show that Fujita's conjecture is true for quasi-elliptic surfaces. Explicitly, for any quasi-elliptic surface $X$ and an ample line bundle $A$ on $X$, we have $K_X + tA$ is base point free for $t \geq 3$ and is very ample for $t \geq 4$.