Periodic Monopoles and Difference Modules / Lecture Notes in Mathematics Bd.2300 (PDF)
(Sprache: Englisch)
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...
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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.
Autoren-Porträt von Takuro Mochizuki
Takuro Mochizuki has been awarded the 2022 Breakthrough Prize in Mathematics for advancing the understanding of holonomic D-modules through his research on harmonic bundles and twister D-modules, which he has studied at the "interface of algebraic geometry and differential geometry".
Bibliographische Angaben
- Autor: Takuro Mochizuki
- 2022, 1st ed. 2022, 324 Seiten, Englisch
- Verlag: Springer Nature Switzerland
- ISBN-10: 3030945006
- ISBN-13: 9783030945008
- Erscheinungsdatum: 23.02.2022
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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