Periodic monopoles and difference modules (Lecture notes in mathematics 2300)

Periodic monopoles and difference modules

Lecture notes in mathematics 2300

単著
数学・物理
望月拓郎(数理解析研究所 / 著者)
Takuro Mochizuki (数理解析研究所, 著者)
出版年月
出版社
Springer
ISBN
9783030944995
本体価格備考
¥8579
頁数
324
本文言語
English

内容紹介

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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