Ample sheaves on moduli schemes

  • Hélène Esnault
  • Eckart Viehweg
Conference paper


In this note we take up methods from [3] and [14], III, to give some criteria for certain direct image sheaves to be ample.


Modulus Space Global Section Effective Divisor Cartier Divisor Invertible Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Esnault, H.: Classification des variétés de dimension 3 et plus. Sém. Bourbaki, Exp. 568, Février 1981. (Lecture Notes Math., Vol 901). Berlin-Heidelberg-New York: Springer 1981Google Scholar
  2. 2.
    Esnault, H., Viehweg, E.: Logarithmic De Eham complexes and vanishing theorems. Invent, math. M, 161–194 (1986)Google Scholar
  3. 3.
    Esnault, H., Vieh weg, E.: Effective hounds for semi positive sheaves and for the height of points on curves over complex function fields. Compos. Math. Ifi, 69–85 (1990)Google Scholar
  4. 4.
    Fujiki, A., Schumacher, G.: The moduli space of extremal compact Kahler manifolds and generalized Weil-Petersson metrics. Publ. RIMS. 26, 101–183 (1990)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Hartshorne, R.: Ample vector bundles. Publ. Math., Inst. Hautes Etud. Sci. 29, 63–94 (1966)MATHMathSciNetGoogle Scholar
  6. 6.
    Kollar, J.: Toward moduli of singular varieties. Compos. Math. 56, 369–398 (1985)MATHMathSciNetGoogle Scholar
  7. 7.
    Kollar, J.: Higher direct images of dualizing sheaves. Ann. Math. 123, 11–42 (1986)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Kollar, J.: Projectivity of complete moduli. J. Differ. Geom. 32, 235–268 (1990)MATHMathSciNetGoogle Scholar
  9. 9.
    Mori, S.: Classification of higher-dimensional varieties. Algebraic Geometry. Bowdoin 1985. Proc. Symp. Pure Math. 46, 269–331 (1987)Google Scholar
  10. Mumford, D.: Abelian Varieties. Tata Inst. Fund. Res., Bombay, and Oxford Univ. Press, 1970Google Scholar
  11. 11.
    Mumford, D., Fogarty, J.: Geometric Invariant Theory, Second Edition. (Ergebnisse der Math., Vol. 34). Berlin-Heidelberg-New York: Springer 1982Google Scholar
  12. 12.
    Pjatetskij-Sapiro, I.I., Safarevich, I.R.: A Torelli theorem for algebraic surfaces of type K3. Math. USSR Izv. 5, 547–588 (1971)CrossRefGoogle Scholar
  13. 13.
    Vieh weg, E.: Vanishing theorems. J. Reine Angew. Math. 235, 1–8 (1982)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Viehweg, E.: Weak positivity and the stability of certain Hilbert points, I. Invent. Math. M, 639–667 (1989), II. Invent. Math. 101, 191–223 (1990), IE. Invent. Math. 101, 521–543 (1990)MATHMathSciNetGoogle Scholar
  15. 15.
    Viehweg, E.: Positivity of sheaves and geometric invariant theory. Proc. of the “A.I. Maltsev Conf.”, Novosibirsk, 1989, to appearGoogle Scholar
  16. 16.
    Viehweg, E.: Quasi-projective quotients by compact equivalence relations. Math. Annalen. to appearGoogle Scholar

Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Hélène Esnault
    • 1
  • Eckart Viehweg
    • 1
  1. 1.Fachbereich 6, MathematikUniversität - GH - EssenEssen 1Germany

Personalised recommendations