A relative Nadel-type vanishing theorem

TL;DR

This paper proves several relative Nadel-type vanishing theorems for Kähler fibrations from complex manifolds to analytic spaces, advancing the understanding of cohomological properties in complex geometry.

Contribution

It introduces new relative vanishing theorems of Nadel type applicable to Kähler fibrations, extending classical results to more general settings.

Findings

Established multiple relative Nadel-type vanishing theorems.

Extended classical vanishing results to Kähler fibrations.

Provided tools for further research in complex algebraic geometry.

Abstract

Let $f:X\rightarrow Y$ be a K\"{a}hler fibration from a complex manifold $X$ to an analytic space $Y$. We show several relative Nadel-type vanishing theorems.