Skip to main content

The irreducibility of the space of curves of given genus

Publications Mathématiques de l'Institut des Hautes Études Scientifiques volume 36, pages 75–109 (1969)Cite this article

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Bibliography

  1. S. Abhyankar, Resolution of singularities of arithmetical surfaces,Proc. Conf. on Arith. Alg. Geom. at Purdue. 1963.

  2. M. Artin, The implicit function theorem in algebraic geometry,Proc. Colloq. Alg. Geom., Bombay, 1968.

  3. M. Artin, Some numerical criteria for contractibility,Am. J. Math.,84 (1962), p. 485.

    Article  MATH  Google Scholar 

  4. J. Benabou, Thèse, Paris, 1966.

  5. F. Enriques andChisini,Teoria geometrica delle equazioni e delle funzioni algebriche, Bologna, 1918.

  6. W. Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves,Ann. of Math. (forthcoming).

  7. J. Giraud,Cohomologie non abélienne, University of Columbia.

  8. A. Grothendieck, Techniques de descente et théorèmes d’existence en géométrie algébrique, IV,Sem. Bourbaki,221, 1960–1961.

  9. R. Hartshorne, Residues and Duality,Springer Lecture Notes,20, 1966.

  10. D. Knutson, Algebraic spaces,Thesis, M.I.T., 1968.

  11. J. Lipman, Rational singularities,Publ. Math. I.H.E.S., no 36 (1969).

  12. M. Lichtenbaum, Curves over discrete valuation rings,Am. J. Math.,90 (1968), p. 380.

    Article  MATH  Google Scholar 

  13. W. Manger, Die Klassen von topologischen Abbildungen einer geschlossenen Fläche auf sich,Math. Zeit.,44 (1939), p. 541.

    Article  Google Scholar 

  14. D. Mumford,Geometric Invariant Theory, Springer-Verlag, 1965.

  15. D. Mumford,Notes on seminar on moduli problems, Supplementary mimeographed notes printed at A.M.S. Woods Hole Summer Institute, 1964.

  16. D. Mumford, Picard groups of moduli problems,Proc. Conf. on Arith. Alg. Geom. at Purdue, 1963.

  17. A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux,Publ. Math. I.H.E.S., no 21.

  18. M. Raynaud, Spécialisation du foncteur de Picard,Comptes rendus Acad. Sci.,264, p. 941 and p. 1001.

  19. I. Šafarevich, Lectures on minimal models,Tata Institute Lectures notes, Bombay, 1966.

  20. M. Schlessinger,Thesis, Harvard.

  21. J.-P. Serre,Rigidité du foncteur de Jacobi d’échelon n ≥ 3, app. à l’exposé 17 du séminaire Cartan 60/61.

  22. F. Severi andLöffler,Vorlesungen über algebraische Geometrie, Teubner, 1924.

  23. A. Weil, Modules des surfaces de Riemann,Sém. Bourbaki, 168, 1957–58.

Download references

Authors
  1. P. Deligne
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Mumford
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first author wishes to thank the Institut des Hautes Études scientifiques, Bures-sur-Yvette, for support in this research andN. Katz, for his invaluable assistance in the preparation of this manuscript; the second author wishes to thank the Tata Institute of Fundamental Research, Bombay, and the Institut des Hautes Études scientifiques.

About this article

Cite this article

Deligne, P., Mumford, D. The irreducibility of the space of curves of given genus. Publications Mathématiques de l’Institut des Hautes Scientifiques 36, 75–109 (1969). https://doi.org/10.1007/BF02684599

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02684599

Keywords

  • Irreducible Component
  • Abelian Variety
  • Finite Type
  • Double Point
  • Stable Curve