Junyan Cao

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math.AG2023

$\partial \partial ˉ$ -lemmas and a conjecture of O. Fujino

Junyan Cao, Mihai Păun

It contains the proof of a very general $\partial \partial ˉ$ -lemma, together with a decomposition theorem for currents with values in a (singular) Hermitian line bundle. As a cor…

math.AG2023

Direct images of pseudoeffective cotangent bundles

Junyan Cao, Andreas Höring

Let A be an elliptic curve, and let $V_{A}$ be the Serre vector bundle on A. A famous example of Demailly-Peternell-Schneider shows that the tautological class of $V_{A}$ contains a un…

math.AG2014

Additivity of the approximation functional of currents induced by Bergman kernels

Junyan Cao

In this note, we give a positive answer to a question raised by Jean-Pierre Demailly in 2013, and show the additivity of the approximation functional of closed positive $(1, 1)$ -cur…

∂∂ˉ-lemmas and a conjecture of O. Fujino

Direct images of pseudoeffective cotangent bundles

Additivity of the approximation functional of currents induced by Bergman kernels

$\partial \partial ˉ$ -lemmas and a conjecture of O. Fujino