Vanishing theorems for pseudo-effective line bundles

TL;DR

This paper proves a broad vanishing theorem for higher direct images of pseudo-effective line bundles on compact K"ahler manifolds, unifying several key results in complex geometry.

Contribution

It introduces a generalized vanishing theorem for pseudo-effective line bundles using numerical dimension, extending previous theorems in the field.

Findings

Establishes a Kawamata-Viehweg-Kollár-Nadel type vanishing theorem

Unifies multiple important vanishing theorems

Applicable to higher direct images of positive currents

Abstract

In the present paper, we establish a general Kawamata-Viehweg-Koll\'ar-Nadel type vanishing theorem for higher direct images in terms of numerical dimension for closed positive currents on compact K\"ahler manifolds, unifying a number of important vanishing theorems.