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A Journey Between Two Curves
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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A Journey Between Two Curves
Інший ID:
2000 Mathematics Subject Classification: 53C28; 53C80; 70H06; 81T30
Посилання:
A Journey Between Two Curves / S.A. Cherkis // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 37 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop on Geometric Aspects of Integrable Systems (July 17–19, 2006, University of Coimbra, Portugal). We thank Pierre Deligne, Tamas Hausel, Nigel Hitchin, Anton Kapustin, Lionel Mason, Tony Pantev, Emma Previato, Samson Shatashvili, and Edward Witten for useful discussions. This work is supported by the Science Foundation Ireland Grant No. 06/RFP/MAT050 and by the European Commision FP6 program MRTN-CT-2004-005104.
Дата:
2007
Переглядів:
653
Завантажень:
248
Анотація:
A typical solution of an integrable system is described in terms of a holomorphic curve and a line bundle over it. The curve provides the action variables while the time evolution is a linear flow on the curve's Jacobian. Even though the system of Nahm equations is closely related to the Hitchin system, the curves appearing in these two cases have very different nature. The former can be described in terms of some classical scattering problem while the latter provides a solution to some Seiberg-Witten gauge theory. This note identifies the setup in which one can formulate the question of relating the two curves.
