On vanishing theorems for analytic spaces

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 Kollár'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.

9 pages. arXiv admin note: substantial text overlap with arXiv:2205.14801, arXiv:2209.06382, v2: minor revisions following referee's comments