Differential operators and rank 2 bundles over elliptic curves
Previato, Emma ; Wilson, George
Compositio Mathematica, Tome 84 (1992), p. 107-119 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1992-01-01
@article{CM_1992__81_1_107_0,
     author = {Previato, Emma and Wilson, George},
     title = {Differential operators and rank $2$ bundles over elliptic curves},
     journal = {Compositio Mathematica},
     volume = {84},
     year = {1992},
     pages = {107-119},
     mrnumber = {1145609},
     zbl = {0758.47038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1992__81_1_107_0}
}

Previato, Emma; Wilson, George. Differential operators and rank $2$ bundles over elliptic curves. Compositio Mathematica, Tome 84 (1992) pp. 107-119. http://gdmltest.u-ga.fr/item/CM_1992__81_1_107_0/

[1] M.F. Atiyah: Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414-452. | MR 131423 | Zbl 0084.17305

[2] H.F. Baker: Note on the foregoing paper 'Commutative ordinary differential operators', by J.L. Burchnall and T.W. Chaundy, Proc. Royal Soc. London (A) 118 (1928), 584-593. | JFM 54.0439.02

[3] J.L. Burchnall and T.W. Chaundy:(a) Commutative ordinary differential operators, Proc. London Math. Soc. 21 (1923), 420-440;(b) Commutative ordinary differential operators, Proc. Royal Soc. London (A) 118 (1928), 557-583;(c) Commutative ordinary differential operators. II, Proc. Royal Soc. London (A) 134 (1932), 471-485. | JFM 57.0478.01 | Zbl 0003.25701

[4] P. Dehornoy: Opérateurs différentiels et courbes elliptiques, Comp. Math. 43 (1981), 71-99. | Numdam | MR 631428 | Zbl 0475.14032

[5] V.G. Drinfeld: On commutative subrings of certain non-commutative rings, Funct. Anal. Appl. 11(1) (1977), 11-14 (Russian), 9-12 (English). | MR 476732 | Zbl 0368.14011

[6] P.G. Grinevich: Rational solutions for the equation of commutation of differential operators, Funct. Anal. Appl. 16(1) (1982), 19-24 (Russian), 15-19 (English). | MR 648805 | Zbl 0514.47034

[7] F.A. Grünbaum: Commuting pairs of linear ordinary differential operators of orders four and six, Physica D 31 (1988), 424-433. | MR 954780 | Zbl 0654.47027

[8] E.L. Ince: Ordinary Differential Equations, Longmans Green and Co., London (1926). | JFM 53.0399.07

[9] I.M. Krichever: Integration of nonlinear equations by methods of algebraic geometry, Funct. Anal. Appl. 11(1) (1977), 15-31 (Russian), 12-26 (English). | MR 1275725 | Zbl 0346.35028

[10] I.M. Krichever: Commutative rings of ordinary differential operators, Funct. Anal. Appl. 12(3) (1978), 20-31 (Russian), 175-185 (English). | MR 509381 | Zbl 0408.34008

[11] I.M. Krichever and S.P. Novikov: Holomorphic bundles over Riemann surfaces and the Kadomtsev-Petviashvili (KP) equation, Funct. Anal. Appl. 12(4) (1978), 41-52 (Russian), 276-286 (English). | MR 515628 | Zbl 0404.35082

[12] I.M. Krichever and S.P. Novikov: Holomorphic fiberings and nonlinear equations. Finite zone solutions of rank 2, Dokl. Akad. Nauk SSSR 247 (1979), 33-37; Soviet Math. Doklady 20 (1979), 650-654. | MR 545939 | Zbl 0434.35078

[13] G. Latham: PhD thesis, Berkeley (1989).

[14] D. Mumford: An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related nonlinear equations, Proc. Int. Symp. on Algebraic Geometry, M. Nagata (ed.), Kinokuniya Book Store, Tokyo (1978). | MR 578857 | Zbl 0423.14007

[15] E. Previato and G. Wilson: Vector bundles over curves and solutions of the KP equations, Proc. Symp. Pure Math. 49 (1989) I, 553-569. | MR 1013152 | Zbl 0697.35128

[16] G.B. Segal and G. Wilson: Loop groups and equations of KdV type, 'Publ. Math. Inst. Hautes Études Sci. 61 (1985), 5-65. | Numdam | MR 783348 | Zbl 0592.35112

[17] J.-L. Verdier: Équations différentielles algébriques, Séminaire Bourbaki 1977-78, Exposé 512 = Lecture Notes in Math. 710, 101-122. | Numdam | MR 554217 | Zbl 0414.14012

[18] G. Wilson: Algebraic curves and soliton equations, in Geometry Today, E. Arbarello, C. Procesi and E. Strickland (eds), Birkhaüser, Boston-Basel- Stuttgart (1985), pp. 303-329. | MR 895160 | Zbl 0581.35065