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Periodic monopoles and difference mo...

Mochizuki, Takuro.

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Periodic monopoles and difference modules

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Periodic monopoles and difference modules/ by Takuro Mochizuki.
作者:	Mochizuki, Takuro.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xviii, 324 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Geometry, Differential. -
電子資源:	https://doi.org/10.1007/978-3-030-94500-8
ISBN:	9783030945008

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 ;v. 2300..

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

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

523835
Geometry, Differential.

LC Class. No.: QA641 / .M63 2022

Dewey Class. No.: 516.36

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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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