Skip to main content
Log in

The structure of the prym map

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

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

Instant access to the full article PDF.

References

  1. Altman, A. &Kleiman, S., Compactifying the Picard Scheme. Part I to appear inAdvances in Math., part II inAmer. J. Math., 101 (1979), 10–41.

    Article  MATH  MathSciNet  Google Scholar 

  2. Andreotti, A. &Mayer, A., On period relations for abelian integrals on algebraic curves.Ann. Scuola Norm. Sup. Pisa, 21 (1967) 189–238.

    MATH  MathSciNet  Google Scholar 

  3. Beauville, A., Prym varieties and the Schottky problem.Invent. Math., 41 (1977), 149–196.

    Article  MATH  MathSciNet  Google Scholar 

  4. —, Variétés de Prym et Jacobiennes intermédiares,Ann. Sci. École Norm. Sup., 10 (1977), 309–391.

    MATH  MathSciNet  Google Scholar 

  5. Clemens, C. H.,Double solids. To appear.

  6. Clemens, C. H. &Griffiths, P. A., The intermediate Jacobian of the cubic threefold.Ann. of Math., 95 (1972), 281–356.

    Article  MATH  MathSciNet  Google Scholar 

  7. Dickson, L. E.,Linear groups, Dover, New York, 1958.

    MATH  Google Scholar 

  8. Deligne, P. & Mumford, D., The irreducibility of the space of curves of given genus.Publ. Math., IHES, Paris, 36 (1969).

  9. Donagi, R., Group law on the intersection of two quadrics.Ann. Scuola Norm. Sup. Pisa, Ser. IV., 7 (1980), 217–239.

    MATH  MathSciNet  Google Scholar 

  10. Enriques, F. & Chisini, O.,Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche. Bologna, 1915–1924.

  11. Fay, J.,Theta functions on Riemann surfaces, Springer Lecture Notes, 352 (1973).

  12. Farkas, H. M., Special divisors and analytic subloci of Teichmueller space.Amer. J. Math., 88 (1966), 881–901.

    Article  MathSciNet  Google Scholar 

  13. Farkas, H. M. &Rauch, H., Period relations of Schottky type on Riemann surfaces.Ann. of Math., 92 (1970), 434–461.

    Article  MATH  MathSciNet  Google Scholar 

  14. Griffiths, P. A., Periods of integrals on algebraic manifolds, II (Local study of the period mapping).Amer. J. Math., 90 (1968), 805–865.

    Article  MATH  MathSciNet  Google Scholar 

  15. Griffiths, P. A. & Harris, J.,Principles of algebraic geometry. Wiley, 1978.

  16. Griffiths, P. A. & Harris, J., Dimension of the variety of special divisors on an algebraic curve. To appear.

  17. Hartshorne, R.,Algebraic Geometry. Springer-Verlag, New York, 1977.

    Google Scholar 

  18. Knutson, D.,Algebraic Spaces. Springer Lecture Notes in Mathematics, 203 (1971).

  19. Kleiman, S. &Laksov, D., On the existence of special divisiors.Amer. J. Math., 94 (1972), 431–436.

    Article  MATH  MathSciNet  Google Scholar 

  20. Mumford, D., Theta characteristics of an algebraic curve,Ann. Sci. École Norm. Sup., 4 (1971), 181–192.

    MATH  MathSciNet  Google Scholar 

  21. —, Prym varieties I, inContributions to Analysis. N.Y., Academic Press, 1974.

    Google Scholar 

  22. —, Stability of projective varieties,Enseignment Math., 23 (1977), 39–110.

    MATH  MathSciNet  Google Scholar 

  23. —,Geometric invariant theory. Berlin-Göttingen-Heidelberg, Springer, 1965.

    MATH  Google Scholar 

  24. Masiewicki, L.,Prym varieties and the moduli space of curves of genus five. Ph.D. Thesis, Columbia Univ., 1974.

  25. Popp, H.,Moduli Theory and Classification Theory of Algebraic Varieties. Springer Lecture Notes in Mathematics, 620 (1977).

  26. Recillas, S., Jacobians of curves with ag 14 are Prym varieties of trigonal curves.Bol. Soc. Mat. Méxicana, 19 (1974), 9–13.

    MATH  MathSciNet  Google Scholar 

  27. Smith, R.,On the degree of the Prym map in dimension five. Ph. D. Thesis, University of Utah, 1977.

  28. Schlessinger, M., Thesis, Harvard University.

  29. Schottky, F. &Jung, H., Neue Sätze über Symmetralfunctionen und die Abelschen Functionen der Riemannschen Theorie,S.-B. Preuss. Akad. Wiss. (Berlin), Phys. Math. Kl. 1 (1909), 282–297.

    Google Scholar 

  30. Schottky, F., Über die Moduln der Thetafunctionen.Acta. Math., 27 (1903), 235–288.

    Article  MATH  Google Scholar 

  31. Semple, J. G. & Roth, L.,Introduction to algebraic geometry. Oxford Univ. Press, 1949.

  32. Tjurin, A., Five lectures on three-dimensional varieties,Russian Math. Surveys, 27 (1972).

  33. —, On the intersections of quadrics.Russian Math. Surveys, 30 (1975), 51–105.

    Article  MATH  MathSciNet  Google Scholar 

  34. Wirtinger, W.,Untersuchungen über Thetafunctionen, Teubner, Berlin, 1895.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

To Gail and Ranwa

Partially supported by NSF Grant #MCS 77-03876.

Partially supported by NSF Grant #MCS 79-03717.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Donagi, R., Smith, R.C. The structure of the prym map. Acta Math 146, 25–102 (1981). https://doi.org/10.1007/BF02392458

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392458

Keywords

Navigation