Partial positivity: geometry and cohomology of q-ample line bundles

TL;DR

This paper reviews partial positivity conditions for line bundles, introduces minor improvements, and presents a new Kodaira-type vanishing theorem for certain divisors and pairs, enhancing understanding of their cohomological properties.

Contribution

It provides an overview of partial positivity, offers minor improvements, and proves a new vanishing theorem for effective q-ample Du Bois divisors and log canonical pairs.

Findings

Introduces a Kodaira-type vanishing theorem for q-ample divisors

Provides minor improvements in the theory of partial positivity

Enhances cohomological understanding of line bundles

Abstract

We give an overview of partial positivity conditions for line bundles, mostly from a cohomological point of view. Although the current work is to a large extent of expository nature, we present some minor improvements over the existing literature and a new result: a Kodaira-type vanishing theorem for effective q-ample Du Bois divisors and log canonical pairs.