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Periodic monopoles and difference modules / Takuro Mochizuki.

9783030945008 (electronic bk.)
3030945006 (electronic bk.)
9783030944995
3030944999

Cham, Switzerland : Springer, 2022.

English

1 online resource (xviii, 324 pages)

10.1007/978-3-030-94500-8 doi

QA641

516.3/6

This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis-Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi-Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity. The theory of periodic monopoles of GCK type has applications to Yang-Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson. This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed March 1, 2022).

Lecture notes in mathematics (Springer-Verlag) ; v. 2300. 1617-9692

Print version: 9783030944995

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