Holomorphic Differentials on Punctured Riemann Surfaces

  • Rainer Dick
Part of the NATO ASI Series book series (NSSB, volume 245)


The investigation of the dynamics of holomorphic or anti-holomorphic X-differentials on Riemann surfaces was initiated by the observation, that these differentials enter string theory via the Faddeev-Popov-procedure, albeit as local sections of Grassmann valued line bundles. Furthermore, it is well known that dual line bundles play an important role in the description of modular deformations of complex structures.


Riemann Surface Line Bundle Theta Function Modular Deformation Pole Order 


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  1. 1.
    L. Alvarez-Gaume, C. Gomez, G. Moore, and C. Vafa, Nucl. Phys. B 303 (1988) 455MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    H. Sonoda, Nucl. Phys. B 281 (1987) 546MathSciNetADSCrossRefGoogle Scholar
  3. T. Eguchi and H. Ooguri, Nucl. Phys. B 282 (1987) 308MathSciNetADSCrossRefGoogle Scholar
  4. 3.
    I. M. Krichever and S. P. Novikov. Funkts. Anal. Prilozhen. 21(2) (1987) 46MathSciNetGoogle Scholar
  5. 4.
    I. M. Krichever and S. P. Novikov, Funkts. Anal. Prilozhen. 21(4) (1987) 47MathSciNetGoogle Scholar
  6. 5.
    L. Bonora, A. Lugo, M. Matone, and J. Russo, Commun. Math. Phys. 123 (1989) 329MathSciNetADSMATHCrossRefGoogle Scholar
  7. 6.
    M. Schlichenmaier: Krichever-Novikov Algebras for More than Two Points, preprint Manusk. Fak. Math. u. Inf. Mannheim 97–1989 (April 1989)Google Scholar
  8. 7.
    R. Dick: Krichever-Novikov-like Bases on Punctured Riemann Surfaces, preprint DESY 89–059 (May 1989), to appear in Lett. Math. Phys.Google Scholar
  9. 8.
    G. Springer: Introduction to Riemann Surfaces. Addison-Wesley. Reading 1957, pp. 272–274MATHGoogle Scholar
  10. 9.
    D. Mumford: Tata Lectures on Theta I, II, Birkhäuser, Boston 1983Google Scholar
  11. 10.
    S. Klimek and A. Lesniewski: Global Laurent Expansions on Riemann Surfaces, preprint HUTMP B 234 (March 1989)Google Scholar
  12. 11.
    J. D. Fay: Theta Functions on Riemann Surfaces, Lecture Notes in Mathematics 352, Springer, Berlin 1973MATHGoogle Scholar
  13. 12.
    J. Lewittes, Acta Math. 111 (1964) 37MathSciNetMATHCrossRefGoogle Scholar
  14. 13.
    L. Mezincescu, R. I. Nepomechie, and C. K. Zachos, Nucl. Phys. B 315 (1989) 43MathSciNetADSCrossRefGoogle Scholar
  15. 14.
    H.Y. Guo. J. S. Na. J. M. Shen, S. K. Wang, and Q. H. Yu: The algebra of meromorphic vector fields and its realization on the space of meromorphic X-differentials on Riemann surface (I), preprint AS-ITP-89–10 (May 1989)Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Rainer Dick
    • 1
  1. 1.II. Institut für Theoretische Physik der Universität HamburgHamburg 50West Germany

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