On coverings of simple abelian varieties

TL;DR

This paper proves that the vector bundle from a finite covering of a simple complex abelian variety is ample, using M-regularity properties, under certain conditions.

Contribution

It establishes a link between finite coverings of simple abelian varieties and the ampleness of associated vector bundles via M-regularity.

Findings

The vector bundle is ample under a necessary condition.

M-regular sheaves are shown to be ample.

The result applies to smooth projective connected finite coverings.

Abstract

We show that the vector bundle associated to a smooth projective connected finite covering of a simple complex abelian variety is ample (under a simple necessary condition). This result is obtained by showing that this bundle is M-regular in the sense of Pareschi-Popa, and that any M-regular sheaf is ample.