Inventiones mathematicae

, Volume 73, Issue 1, pp 139–150 | Cite as

Every K3 surface is Kähler

  • Y. -T. Siu


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  1. 1.
    Bishop, E.: Conditions for the analyticity of certain sets. Michigan Math. J.11, 289–304 (1964)Google Scholar
  2. 2.
    Burns, D., Rapoport, M.: On the Torelli problem for Kähler K3 surfaces. Ann. Scient. Éc. Norm. Sup.8, 235–274 (1975)Google Scholar
  3. 3.
    Dunford, N., Schwartz, J.T.: Linear Operators, Vol. I. New York: Interscience 1958Google Scholar
  4. 4.
    Harvey, F.R., Lawson, B.: An intrinsic characterization of Kähler manifolds.Google Scholar
  5. 5.
    Hitchin, N.: Compact four-dimensional Einstein manifolds. J. Diff. Geom.9, 435–441 (1974)Google Scholar
  6. 6.
    Kodaira, K.: On the structure of compact complex analytic surfaces, I. Amer. J. Math.86, 751–798 (1964)Google Scholar
  7. 7.
    Kodaira, K., Morrow, J.: Complex Manifolds. New York: Holt, Rinehart & Winston 1971Google Scholar
  8. 8.
    Kodaira, K., Spencer, D.C.: On deformations of complex analytic structures, III. Stability theorems for complex structures. Ann. of Math.71, 43–76 (1960)Google Scholar
  9. 9.
    Kulikov, V.: Epimorphicity of the period mapping for surfaces of type K3. Uspehi Mat. Nauk32, (No. 4) 257–258 (1977)Google Scholar
  10. 10.
    Looijenga, E.: A Torelli theorem for Kähler-Einstein K3 surfaces. Lecture Notes in Math Vol. 892, pp. 107–112. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  11. 11.
    Looijenga, E., Peters, C.: Torelli theorems for Kähler K3 surfaces. compositio Math.42, 145–186 (1981)Google Scholar
  12. 12.
    Miyaoka, Y.: Kähler metrics on elliptic surfaces. Proc. Japan Acad.50, 533–536 (1974)Google Scholar
  13. 13.
    Morrey, C.B., Jr.: Multiple integrals in the calculus of variations. New York: Springer 1966Google Scholar
  14. 14.
    Piatetskii-Shapiro, I.I., Shafarevitch, I.R.: A Torelli theorem for algebraic surfaces of type K3. Izv. Akad. Nauk SSSR35, 547–572 (1971); (English Translation) Math. USSR Izvestija5, 547–588 (1971)Google Scholar
  15. 15.
    Siu, Y.-T.: A simple proof of the surjectivity of the period map of K3 surfaces. Manuscripta Math.35, 311–321 (1981)Google Scholar
  16. 16.
    Sommese, A.J.: Quaternionic manifolds. Math. Ann.212, 191–214 (1975)Google Scholar
  17. 17.
    Sullivan, D.: Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math.36, 225–255 (1976)Google Scholar
  18. 18.
    Todorov, A.N.: Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces. Invent. Math.61, 251–265 (1980)Google Scholar
  19. 19.
    Yau, S.-T.: On the Ricci curvature of a compact Kähler manifold, and the complex Monge-Ampère equation, I. Comm. Pure Applied Math.31, 339–411 (1978)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Y. -T. Siu
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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