Anti-ample bundle, nef vector bundle, big vector bundle

TL;DR

This paper proves that the direct image of an anti-ample vector bundle remains anti-ample under finite flat morphisms and explores properties of big and nef vector bundles, including tensor product behavior.

Contribution

It establishes the anti-ampleness preservation under finite flat morphisms and generalizes known results about nef and big vector bundles.

Findings

Direct image of anti-ample bundle is anti-ample under finite flat morphisms

Tensor product of nef and big bundles is nef and big

Generalizes Schneider's result on nef and big bundles

Abstract

We prove that the direct image of an anti-ample vector bundle is anti-ample under any finite flat morphism of non-singular projective varieties. In the second part we prove some properties of big and nef vector bundles. In particular it is shown that the tensor product of a nef vector bundle with a nef and big vector bundle is again nef and big. This generalizes a result of Schneider.