Construction of the Jacobi Variety for the Spectral Curve

  • Sebastian Klein
Part of the Lecture Notes in Mathematics book series (LNM, volume 2229)


In the present chapter, we will construct Jacobi coordinates for the spectral curve Σ, which can have singularities, is non-compact, and has always infinite arithmetic genus and generally infinite geometric genus. For the construction of the Jacobi variety, the estimates proven in the preceding two chapters will play an important role.


  1. [Fa-K]
    H. Farkas, I. Kra, Riemann Surfaces, 2nd edn. (Springer, New York, 1992)CrossRefGoogle Scholar
  2. [Fe-K-T]
    J. Feldman, H. Knörrer, E. Trubowitz, Riemann Surfaces of Infinite Genus (American Mathematical Society, Providence, 2003)CrossRefGoogle Scholar
  3. [Hi]
    N.J. Hitchin, Harmonic maps from a 2-torus to the 3-sphere. J. Differ. Geom. 31, 627–710 (1990)MathSciNetCrossRefGoogle Scholar
  4. [McK-T]
    H. McKean, E. Trubowitz, Hill’s operator and hyperelliptic function theory in the presence of infinitely many branch points. Commun. Pure Appl. Math. 29, 143–226 (1976)MathSciNetCrossRefGoogle Scholar
  5. [Ro]
    M. Rosenlicht, Generalized Jacobian varieties. Ann. Math. 59, 505–530 (1954)MathSciNetCrossRefGoogle Scholar
  6. [Se]
    J.-P. Serre, Algebraic Groups and Class Fields (Springer, New York, 1988)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sebastian Klein
    • 1
  1. 1.School of Business Informatics & MathematicsUniversity of MannheimMannheimGermany

Personalised recommendations