On vanishing theorems for analytic spaces

TL;DR

This paper presents new vanishing theorems for projective morphisms between complex analytic spaces, generalizing Kollár's results and aiding the study of minimal models in complex analysis.

Contribution

It introduces a complex analytic generalization of Kollár's torsion-freeness and vanishing theorem for simple normal crossing pairs.

Findings

Established a new vanishing theorem for projective morphisms in complex analytic spaces

Generalized Kollár's torsion-freeness theorem to the analytic setting

Contributed to the understanding of minimal models in complex analysis

Abstract

This is a short report on our new vanishing theorems for projective morphisms between complex analytic spaces. We established a complex analytic generalization of Koll\'ar's torsion-freeness and vanishing theorem for analytic simple normal crossing pairs. Although our results may look artificial, they have already played a crucial role for the study of minimal models in the complex analytic setting.