On the $q$-ampleness of the tensor product of two line bundles

TL;DR

This paper proves that the tensor product of a q-ample line bundle and another with a small base locus remains q-ample, extending understanding of positivity properties in algebraic geometry.

Contribution

It establishes that the tensor product preserves q-ampleness under conditions on the base locus, a new result in the theory of line bundle positivity.

Findings

Tensor product of q-ample line bundle with low base locus remains q-ample.

Provides conditions under which q-ampleness is preserved.

Enhances understanding of positivity properties in algebraic geometry.

Abstract

We prove that the tensor product of two line bundles, one being $q$-ample and the other with sufficiently low-dimensional base locus, is still $q$-ample.