Periodic Monopoles and Difference Modules Lecture Notes in Mathematics 1st editon by Takuro Mochizuki 3030945006 9783030945008

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ISBN 10: 3030945006
ISBN 13: 9783030945008
Author: Takuro Mochizuki

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 graduatestudents and researchers in differential and algebraic geometry, as well as in mathematical physics.

Periodic Monopoles and Difference Modules Lecture Notes in Mathematics 1st Table of contents:

1. Introduction

2. Preliminaries

3. Formal Difference Modules and Good Parabolic Structure

4. Filtered Bundles

5. Basic Examples of Monopoles Around Infinity

6. Asymptotic Behaviour of Periodic Monopoles Around Infinity

7. The Filtered Bundles Associated with Periodic Monopoles

8. Global Periodic Monopoles of Rank One

9. Global Periodic Monopoles and Filtered Difference Modules

10. Asymptotic Harmonic Bundles and Asymptotic Doubly Periodic Instantons (Appendix)

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Takuro Mochizuki,Periodic Monopoles,Difference Modules,Lecture Notes