Monopoles and Modifications of Bundles over Elliptic Curves
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Monopoles and Modifications of Bundles over Elliptic Curves
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| Creator |
Levin, A.M.
Olshanetsky, M.A. Zotov, A.V. |
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| Description |
Modifications of bundles over complex curves is an operation that allows one to construct a new bundle from a given one. Modifications can change a topological type of bundle. We describe the topological type in terms of the characteristic classes of the bundle. Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. Following Kapustin and Witten we define the modifications in terms of monopole solutions of the Bogomolny equation. We find the Dirac monopole solution in the case R × (elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it generalizing the Kronecker results. We use it to define Abelian modifications for bundles of arbitrary rank. We also describe non-Abelian modifications in terms of theta-functions with characteristic.
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| Date |
2019-02-19T17:47:50Z
2019-02-19T17:47:50Z 2009 |
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| Type |
Article
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| Identifier |
Monopoles and Modifications of Bundles over Elliptic Curves / A.M. Levin, M.A. Olshanetsky, A.V. Zotov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 21 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 14H70; 14F05; 33E05; 37K20; 81R12 http://dspace.nbuv.gov.ua/handle/123456789/149154 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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