2007/01/15 by H. W. Braden, Yu. N. Fedorov
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #math-ph #math.AG #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.geomphys.2008.05.009
11 pages
arxiv created 2007/01/15 · openalex publication_date 2008/05/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve the problem of inversion of an extended Abel-Jacobi map ∫_P0^P1ω+...+∫_P0^Pg+n-1ω=\bf z, ∫_P0^P1Ωj1+... +∫_P0^Pg+n-1Ωj1 =Zj, j=2,...,n, where Ωj1 are (normalised) abelian differentials of the third kind. In contrast to the extensions already studied, this one contains meromorphic differentials having a common pole Q1. 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.