Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities


Author: Shin-ichi Matsumura
Journal: J. Algebraic Geom. 27 (2018), 305-337
DOI: https://doi.org/10.1090/jag/687
Published electronically: August 17, 2017
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Abstract | References | Additional Information

Abstract: The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel type vanishing theorem. For the proof, we study the asymptotic behavior of the harmonic forms with respect to a family of regularized metrics, and give a method to obtain $ L^{2}$-estimates of solutions of the $ \overline {\partial }$-equation by using the de Rham-Weil isomorphism between the $ \overline {\partial }$-cohomology and the $ \rm {\check {C}}$ech cohomology.


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Additional Information

Shin-ichi Matsumura
Affiliation: Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan
Email: mshinichi@m.tohoku.ac.jp, mshinichi0@gmail.com

DOI: https://doi.org/10.1090/jag/687
Received by editor(s): December 21, 2015
Received by editor(s) in revised form: February 4, 2016
Published electronically: August 17, 2017
Additional Notes: The author was partially supported by Grant-in-Aid for Young Scientists (B) #25800051, (A) #17H04821 from JSPS, and the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers
Article copyright: © Copyright 2017 University Press, Inc.

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