Deformations of curves I moduli for hyperelliptic curves

  • O. A. Laudal
  • K. Lønsted
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 687)


Irreducible Component Commutative Diagram Local Ring Hyperelliptic Curve Weierstrass Point 
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  1. 1.
    Accola, R.D.M.: Riemann Surfaces, Theta Functions, and Abelian Automorphisms Groups, Springer Lecture Notes 483, 1975.Google Scholar
  2. 2.
    Arbarello, E.: Weierstrass Points and Moduli of Curves, Compositio Math. 29 (1974), 325–342.MathSciNetzbMATHGoogle Scholar
  3. 3.
    Deligne, P. and Mumford, D.: The irreducibility of the space of curves of given genus, Publ. Math. de l'I.H.E.S. 36 (1969), 75–110.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Farkas, H.M.: Special Divisors and Analytic Subloci of Teichmüller Space, Amer. J. Math. 88 (1966), 881–901.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Grothendieck, A.: Fondéments de la Géométrie Algébrique (FGA), Extraits du Sém. Bourbaki 1957–62, Secrétariat Mathématique, Paris, 1962.Google Scholar
  6. 6.
    Grothendieck, A.: Séminaire de Géométrie Algébrique 1960/61 (SGA 1). Revêtements Etale et Groupe Fondamental, Springer Lecture Notes 224, 1971.Google Scholar
  7. 7.
    Grothendieck, A. et Dieudonné, J.: Eléments de Géométrie Algébrique, Chap. IV4, Publ. Math. de l'I.H.E.S. 32 (1967).Google Scholar
  8. 8.
    Hurwitz, A.: Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 39 (1891), 1–61.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lange, H.: Kurven mit rationaler Abbildung, Göttingen Habilitationsschrift, 1975.Google Scholar
  10. 10.
    Laudal, O.A.: Sections of Functors and the Problem of Lifting (Deforming) Algebraic Structures, Inst. Math. Univ. Oslo Preprint Ser. nr. 18, 1975.Google Scholar
  11. 11.
    Laudal, O.A.: A generalized Tri-secant Lemma, in Proceedings of a Symposium on algebraic Geometry, Univ. Tromsö, July 1977, Springer Lecture Notes (this volume).Google Scholar
  12. 12.
    Lønsted, K.: The hyperelliptic locus with special reference to characteristic two, Math. Ann. 222 (1976), 55–61.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lønsted, K. and Kleiman, S.L.: Basics on Families of hyperelliptic curves, Københavns Univ. Mat. Inst. Preprint Ser. 1977 no. 7, March 1977.Google Scholar
  14. 14.
    Mumford, D.: Lectures on Curves on an Algebraic Surface, Annals of Math. Studies 59, Princeton Univ. Press, 1970.Google Scholar
  15. 15.
    Mumford, D.: Geometric Invariant Theory, Ergebnisse d. Math., Bd. 34, Springer Verlag 1965.Google Scholar
  16. 16.
    Oort, F.: Fine and Coarse Moduli Schemes are different, Report 74-10, Dept. Math., Univ. of Amsterdam, 1974 (partly published in Séminaire d'Algèbre Paul Dubreil Paris 1975–76, Springer Lecture Notes 586, 1977).Google Scholar
  17. 17.
    Popp, H.: The singularities of the moduli scheme of curves, J. Number Theory 1(1969), 90–107.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Rauch, H.E.: Weierstrass Points, Branch Points, and the Moduli of Riemann Surfaces, Comm. Pure a. Appl. Math. 12 (1959), 543–560.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • O. A. Laudal
    • 1
  • K. Lønsted
    • 2
  1. 1.Universitetet i Oslo Matematisk InstitutNorway
  2. 2.Matematisk InstitutUniversitetsparken 5København ØDenmark

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