On vanishing and torsion-freeness results for adjoint pairs

TL;DR

This paper establishes new vanishing and torsion-freeness theorems for higher direct images of adjoint pairs under certain conditions, with applications to generic vanishing and weak positivity.

Contribution

It introduces novel vanishing and torsion-freeness results for adjoint pairs satisfying relative abundance and nefness, advancing the understanding of their higher direct images.

Findings

Proved vanishing theorems for higher direct images.

Established torsion-freeness under specific conditions.

Applied results to generic vanishing and weak positivity.

Abstract

We prove some vanishing and torsion-freeness results for higher direct images of adjoint pairs satisfying relative abundance and nefness conditions. These are applied to generic vanishing and weak positivity.