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Periodic Monopoles and Difference Modules (Paperback, 1st ed. 2022)
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Periodic Monopoles and Difference Modules (Paperback, 1st ed. 2022)
Series: Lecture Notes in Mathematics, 2300
Expected to ship within 10 - 15 working days
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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
graduate students and researchers in differential and algebraic
geometry, as well as in mathematical physics.
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