Abstract
Let (X, ω) be a compact Hermitian manifold of complex dimension n. In this article, we first survey recent progress towards Grauert-Riemenschneider type criteria. Secondly, we give a simplified proof of Boucksom’s conjecture given by the author under the assumption that the Hermitian metric ω satisfies \(\partial \overline \partial {\omega ^l} = {\rm{for}}\;{\rm{all}}\;l\), i.e., if T is a closed positive current on X such that ∫X\(T_{ac}^n>0\), then the class {T} is big and X is Kahler. Finally, as an easy observation, we point out that Nguyen’s result can be generalized as follows: if \(\partial \overline \partial \omega = 0\), and T is a closed positive current with analytic singularities, such that ∫X\(T_{ac}^n>0\), then the class {T} is big and X is Kahler.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.