An extended Abel-Jacobi map

JOURNAL OF GEOMETRY AND PHYSICS

卷:58

Article

Braden, H. W.²  Fedorov, Yu. N.¹ 

[1] Univ Politecn Cataluna, Dept Math 1, E-08028 Barcelona, Catalunya, Spain

[2] Univ Edinburgh, Sch Math, Edinburgh, Midlothian, Scotland

关键词: Generalized Abel map;    Theta functions;    Integrability;    Monopoles;   

DOI  :  10.1016/j.geomphys.2008.05.009

来源: Elsevier

【 摘 要 】

We solve the problem of inversion of an extended Abel-Jacobi map integral(P1)(P0) omega + ... + integral(Pg+n-1)(P0) omega = Z, integral(P1)(P0) Omega(j1) + ... + integral(Pg+n-1)(P0) Omega(j1) = Z(j), j = 2.....n. where Omega(j1), are (normalized) Abelian differentials of the third kind. In contrast to the extensions already studied, this one contains meromorphic differentials having a common pole Q(1). This inversion problem arises in algebraic geometric description of monopoles, as well as in the linearization of integrable systems on finite-dimensional unreduced coadjoint orbits on loop algebras. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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