New characterizations of plurisubharmonic functions and positivity of direct image sheaves

Abstract

We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of generalized Bergman kernel metrics and Griffiths positivity of the direct images of twisted relative canonical bundles associated to holomorphic families of Kähler manifolds.

References in corpus (4)

• Optimal constant in an L^2 extension problem and a proof of a conjecture of Ohsawa
• Bergman kernels and subadjunction
• Strong openness of multiplier ideal sheaves and optimal $L^2$ extension
• Complex Brunn-Minkowski theory and positivity of vector bundles

Cited by in corpus (10)

• Positivity of holomorphic vector bundles in terms of $L^p$-conditions of $\bar{\partial }$
• Canonical bundle formula and degenerating families of volume forms
• A converse of Hörmander's $L^2$-estimate and new positivity notions for vector bundles
• Linear invariants of complex manifolds and their plurisubharmonic variations
• Pseudonorms on direct images of pluricanonical bundles
• Boundary asymptotics of the relative Bergman kernel metric for curves
• A simplified proof of optimal $L^2$-extension theorem and extensions from non-reduced subvarieties
• Structure of projective varieties with nef anticanonical divisor: the case of log terminal singularities
• Optimal $L^2$-extensions on tube domains and a simple proof of Prékopa's theorem
• Nakano Positivity of direct image sheaves of adjoint line bundles with mild singularities