Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Positivity of twisted relative pluricanonical bundles and their direct images


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
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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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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

DOI: https://doi.org/10.1090/jag/702
Received by editor(s): March 9, 2015
Published electronically: December 15, 2017
Article copyright: © Copyright 2017 University Press, Inc.

American Mathematical Society