On vanishing theorems for analytic spaces
Osamu Fujino

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Holomorphic and Operator Theory
