Positivity of twisted relative pluricanonical bundles and their direct images

Păun, Mihai; Takayama, Shigeharu

doi:10.1090/jag/702

Authors: Mihai Păun and Shigeharu Takayama
Journal: J. Algebraic Geom. 27 (2018), 211-272
DOI: https://doi.org/10.1090/jag/702
Published electronically: December 15, 2017
MathSciNet review: 3764276
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Abstract | References | Additional Information

Abstract: Our main goal in this article is to establish a metric version of the positivity properties of twisted relative pluricanonical bundles and their direct images. Some of the important technical points of our proof are an $L^{2/m}$-extension theorem of Ohsawa-Takegoshi type which is derived from the original result by a simple fixed point method and the notion of “singular Hermitian metric” on vector bundles, together with an appropriate definition of positivity of the associated curvature. Part of this article is based on the joint work of the first-named author with Bo Berndtsson, and it can be seen as an expanded and updated version of it.

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Additional Information

Mihai Păun
Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607
Email: mpaun@uic.edu

Shigeharu Takayama
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan
Email: taka@ms.u-tokyo.ac.jp

Received by editor(s): March 9, 2015
Published electronically: December 15, 2017
Article copyright: © Copyright 2017 University Press, Inc.