$\partial \bar{\partial }$-lemmas and a conjecture of O. Fujino

Abstract

It contains the proof of a very general $\partial \bar{\partial }$-lemma, together with a decomposition theorem for currents with values in a (singular) Hermitian line bundle. As a corollary, we establish the Kähler version on an injectivity theorem due to O. Fujino in the projective case.

Comments welcome! We have decided to split into two parts our previous work arXiv:2012.05063. This is the second part