Vector bundles and lax equations on algebraic curves

Communications in Mathematical Physics

Volumn 229, Issue 2, 2002, Pages 229-269

  Krichever, I ^a,b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036706640     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200659     Document Type: Article

References (22)

1. Krichever, I.M., Novikov, S.P.: Holomorphic bundles over algebraic curves and non-linear equations Uspekhi Mat. Nauk 35, n 6 (1980)
2. Hitchin, N.: Stable bundles and integrable systems. Duke Math. Journ. 54, (1), 91-114 (1987)
3. Krichever, I.M., Novikov, S.P.: Holomorphic bundles over Riemann surfaces and Kadomtzev-Petviashvilii equation. Funk. anal. i pril. 12, n 4, 41-52 (1978)
4. Zakharov, V., Shabat, A.: Integration of non-linear equations of mathematical physics by the method of the inverse scattering problem. II. Funct. Anal. and Appl. 13, 13-22 (1979)
5. Ben-Zvi, D., Frenkel, E.: Spectral Curves, Opers and Integrable Systems. math.AG/9902068
6. Tyurin, A.: Classification of vector bundles over an algebraic curve of arbitrary genus. Amer. Math. Soc. Translat. II, Ser 63, 245-279 (1967)
7. Krichever, I.M.: The commutative rings of ordinary differential operators. Funk. anal. i pril. 12, n 3, 20-31 (1978)
8. Enriquez, E., Rubtsuv, V.: Hecke-Tyurin parametrization of the Hitchin and KZB systems. math. AG/9911087
9. Krichever, I., Phong, D.H.: On the integrable geometry of N = 2 supersymmetric gauge theories and soliton equations. J. Differential Geometry 45, 445-485 (1997); hep-th/9604199
10. Krichever I., Phong, D.H.: Symplectic forms in the theory of solitons. In: Surveys in Differential Geometry IV, edited by C.L. Terng and K. Uhlenbeck, Cambridge: International Press, 1998, pp. 239-313; hep-th/9708170
11. Krichever, I.M.: Elliptic solutions to difference non-linear equations and nested Bethe ansatz. solv-int/9804016.
12. Gorsky, A., Nekrasov, N.: Elliptic Calogero-Moser system from two-dimensional current algebra. Preprint ITEP-NG/1-94. hep-th/9401021.
13. Krichever, I.M.: The algebraic-geometrical construction of Zakharov-Shabat equations and their periodic solutions. Doklady Acad. Nauk USSR 227, n 2, 291-294 (1976)
14. Krichever, I.: The integration of non-linear equations with the help of algebraic-geometrical methods. Funk. Anal. i Pril. 11, n 1, 15-31 (1977)
15. Krichever, I.M.: Elliptic solutions of Kadomtsev-Petviashvilii equation and integrable systems of particles. Funct. Anal. App. 14, n 4, 282-290 (1980)
16. Krichever, I., Phong, D.H.: Spin Chain Models with Spectral Curves from M Theory. Commun. Math. Phys. 213, 539-574 (2000)
17. Novikov, S.P., Veselov, A.P.: On Poisson brackets compatible with algebraic geometry and Korteweg-deVries dynamics on the space of finite-zone potentials. Soviet Math. Doklady 26, 357-362 (1982)
18. Nekrasov, N.: Holomorphic Bundles and Many-Body systems. Commun. Math. Phys. 180, 587-604 (1996)
19. McKean, H., Trubovitz, E.: Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points. Comm. Pure Appl. Math. 29, 143-226 (1976)
20. Krichever I.: Spectral theory of two-dimensional periodic operators and its applications. Uspekhi Mat. Nauk 44, n 2, 121-184 (1989)
21. Felder, J., Knörrer, H., Trubowitz, E.: Riemann surfaces of the infinite genus. Preprint ETH Zurich
22. Marchenko, V., Ostrovski, I.: In the book: V. Marchenko, Sturm-Liouville operator and applications. Nukova Dumka, 1977 (in Russian)