How Many Kähler Metrics Has a K-3 Surface?

  • A. N. Todorov
Part of the Progress in Mathematics book series (PM, volume 36)


The aim of this article is to prove the following theorem:


Modulus Space Dense Subset Fundamental Domain Einstein Metrics Ample Divisor 
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. [B R]
    D. Burns and M. Rapoport, On the Torelli problem for Kählerian K-3 surfaces, Arm. Sci. Ecole Norm. Sup. 4, ser. 8 (1975).Google Scholar
  2. [H]
    N. Hitchin, Compact four-dimensional Einstein manifolds, Journal of Differential Geometry, 435–441 (1974).Google Scholar
  3. [Sh]
    I. R. Shafarevich, Algebraic surfaces, Proc. Steklov Inst., vol. 75 (1965).Google Scholar
  4. [S P]
    Shafarevich and Piatetski-Shapiro, A Torelli theorem for algebraic surfaces of type K-3, Izv. Akad. Nauk 35, 530–365 (1971).Google Scholar
  5. [T]
    A. Todorov, Application of Kähler-Einstein-Calabi-Yau metric to Moduli of K-3 surfaces, Inventiones Math., 61, 251–265 (1980).zbMATHCrossRefGoogle Scholar
  6. T2] A. Todorov, The moduli space of Einstein metrics on a K-3 surface, To appear in a Proc. of a conference in math. physics Promorsko.Google Scholar
  7. [Yau]
    S. T. Yau, On the Ricci curvature of a compact Kähler manifold and the Monge-Ampere equation 1, Comm. Pure Appl. Math. XXXI, 339–411 (1978).Google Scholar
  8. [W]
    A. Weil, Collected papers, vol. 2, 365–395, Springer-Verlag 1979.Google Scholar
  9. [Siu]
    Y. T. Siu, A simple proof of the surjectivity of the period map for K-3 surfaces, Manuscripta Math. 35, 311–321 (1981).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • A. N. Todorov
    • 1
  1. 1.Bulgarian Academy of SciencesBAN Institute of Math.SofiaBulgaria

Personalised recommendations