Families of compact Riemann surfaces which do not admit nth roots

  • Patricia L. Sipe
Conference paper
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 11)

Abstract

Let π : VB be a holomorphic family of compact Riemann surfaces of genus p ≥ 2 (to be defined in section 1). For any t ? B, the fiber X t = π-1(t) is a closed Riemann surface; the canonical line bundle K(X t ) is the holomorphic cotangent bundle of X t . A standard construction (see section 1 for details) produces a line bundle K rel(V) → V, called the relative canonical bundle, whose restriction to each Riemann surface X t V is equivalent to the canonical bundle K(X t ). (Throughout this paper, all line bundles will be holomorphic complex line bundles and equivalence will be holomorphic equivalence.)

Keywords

Manifold 

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References

  1. 1.
    Farkas, H. and Kra, I., “Riemann Surfaces,” Springer-Verlag, New York, 1980.MATHGoogle Scholar
  2. 2.
    Sipe, P.L., Roots of the canonical bundle of the universal Teichmuller curve and certain subgroups of the mapping class groups Math. Ann. 260 (1982), 67–92.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Sipe, P.L., Some finite quotients of the mapping class group of a surface ,Proceedings of the American Mathematical Society 97 (1986), 515–524.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Patricia L. Sipe
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

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