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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Kobayashi-Hitchin correspondence for analytically stable bundles


Author: Takuro Mochizuki
Journal: Trans. Amer. Math. Soc. 373 (2020), 551-596
MSC (2010): Primary 53C07, 14D21
DOI: https://doi.org/10.1090/tran/7956
Published electronically: October 1, 2019
MathSciNet review: 4042885
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Abstract: We prove the existence of an Hermitian-Einstein metric on holomorphic vector bundles with an Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying Kähler manifolds. We also study the curvature decay of the Hermitian-Einstein metrics. It is useful for the study of the classification of instantons and monopoles on the quotients of four-dimensional Euclidean space by some types of closed subgroups. We also explain examples of doubly periodic monopoles corresponding to some algebraic data.


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Additional Information

Takuro Mochizuki
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: takuro@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/tran/7956
Received by editor(s): January 20, 2018
Received by editor(s) in revised form: January 2, 2019, and June 30, 2019
Published electronically: October 1, 2019
Additional Notes: The author was partially supported by the Grant-in-Aid for Scientific Research (S) (No. 17H06127), the Grant-in-Aid for Scientific Research (S) (No. 16H06335), and the Grant-in-Aid for Scientific Research (C) (No. 15K04843), Japan Society for the Promotion of Science.
Part of this study was done during the author’s stay at the University of Melbourne, and he is grateful to Kari Vilonen and Ting Xue for their excellent hospitality and their support.
Article copyright: © Copyright 2019 American Mathematical Society