New characterizations of plurisubharmonic functions and positivity of direct image sheaves

2018/09/27 by Deng, Fusheng, Wang, Zhiwei, Zhang, Liyou +1 · 3 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.10371

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.

Cited by

• Compact Kähler manifolds with nef anti-canonical bundle
• An optimal L² extension for continuous L²-optimal Hermitian metrics
• An Ohsawa-Takegoshi-type L² extension for upper semi-continuous L²-optimal functions

Related

• Positivity of twisted relative pluricanonical bundles and their direct images
• Positivity of direct image bundles and convexity on the space of Kahler metrics
• Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric
• Singular Hermitian metrics and positivity of direct images of\n pluricanonical bundles
• Characterizations of Griffiths Positivity, Pluriharmonicity and Flatness