On semipositivity, injectivity and vanishing theorems

Abstract

This is a survey article on the recent developments of semipositivity, injectivity, and vanishing theorems for higher-dimensional complex projective varieties.

41 pages, survey article written for Zucker 65, comments are welcome, v2: I mainly revised Subsection 3.1, v3: revision following referee's comments, v4: final version, references and address were updated

References in corpus (7)

• A Bergman kernel proof of the Kawamata subadjunction theorem
• Injectivity theorem for pseudo-effective line bundles and its applications
• Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension
• Versions of injectivity and extension theorems
• A vanishing theorem of Koll'ar-Ohsawa type
• Kollár--Nadel type vanishing theorem
• Vanishing and semipositivity theorems for semi-log canonical pairs

Cited by in corpus (5)

• Injectivity theorem for pseudo-effective line bundles and its applications
• A vanishing theorem of Koll'ar-Ohsawa type
• Vanishing and semipositivity theorems for semi-log canonical pairs
• On log canonical rational singularities
• Some Kollar-Enoki type injectivity and Nadel type vanishing theorems on compact Kahler manifolds