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Periodic monopoles and difference modules

Record Type:	Electronic resources : Monograph/item
Title/Author:	Periodic monopoles and difference modulesby Takuro Mochizuki.
Author:	Mochizuki, Takuro.
Published:	Cham :Springer International Publishing :2022.
Description:	xviii, 324 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Differential.
Online resource:	https://doi.org/10.1007/978-3-030-94500-8
ISBN:	9783030945008$q(electronic bk.)

Periodic monopoles and difference modules
Mochizuki, Takuro.

Periodic monopoles and difference modules[electronic resource] /by Takuro Mochizuki. - Cham :Springer International Publishing :2022. - xviii, 324 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23001617-9692 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783030945008$q(electronic bk.)

Standard No.: 10.1007/978-3-030-94500-8doiSubjects--Topical Terms:

182610
Geometry, Differential.

LC Class. No.: QA641 / .M63 2022

Dewey Class. No.: 516.36

Periodic monopoles and difference modules
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520 $a 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.
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