Wang Xu

On the positivity of direct image bundles. II

We show that if an upper semi-continuous function $\varphi$ on $\Omega\in\mathbb C^n$ satisfies some natural conditions, and for any non-negative psh function $\psi$ on $\mathbb D\times]Omega$, the fiberwise Bergman kernel associated to $p_2^*\varphi+\psi$ is log-psh, then $\varphi$ must be psh. This offers a version o...