Inventiones mathematicae

, Volume 75, Issue 1, pp 105–121 | Cite as

On K3 surfaces with large Picard number

  • D. R. Morrison


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Burns, D., Rapoport, M.: On the Torelli problem for Kählerian K3 surfaces. Ann. Scient. Ec. Norm. Sup.8, 235–274 (1975)Google Scholar
  2. 2.
    Hodge, W.V.D.: The topological invariants of algebraic varieties. Proc. Intern. Cong. Math. Cambridge1, 182–192 (1950)Google Scholar
  3. 3.
    Kneser, M.: Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen. Arch. Math. (Basel)7, 323–332 (1956)Google Scholar
  4. 4.
    Kodaira, K.: On the structure of compact complex analytic surface, I. Amer. J. Math.86, 751–798 (1964)Google Scholar
  5. 5.
    Kulikov, V.: Epimorphicity of the period mapping for surfaces of type K3., (in Russian) Uspehi Mat. Nauk.32, (4) 257–258 (1977)Google Scholar
  6. 6.
    Looijenga, E.: A Torelli theorem for Kähler-Einstein K3 surfaces. Lecture Notes in Mathematics, vol. 894, 107–112. Berlin-Heidelberg-New York: Springer 1981Google Scholar
  7. 7.
    Looijenga, E., Peters, C.: Torelli theorems for Kähler K3 surfaces. Compositio Math.42, 145–186 (1981)Google Scholar
  8. 8.
    Milnor, J.: On simply connected 4-manifolds. Symposium Internacional de Topologia Algebraica, La Universidad Nacional Autónoma de México y la UNESCO pp. 122–128, 1958Google Scholar
  9. 9.
    Namikawa, Y.: Surjectivity of period map for K3 surfaces. Classification of algebraic and analytic manifolds, Progress in Mathematics, vol. 39, 379–397, Boston-Basel-Stuttgart: Birkhäuser 1983Google Scholar
  10. 10.
    Nikulin, V.: On Kummer surfaces. Izv. Akad. Nauk SSSR39, 278–293 (1975); Math. USSR Izvestija9, 261–275 (1975)Google Scholar
  11. 11.
    Nikulin, V.: Finite groups of automorphisms of Kählerian surfaces of type K3. Trudy Mosk. Mat. Ob.38, 75–137 (1979), Trans. Moscow Math. Soc.38, 71–135 (1980)Google Scholar
  12. 12.
    Nikulin, V.: Integral symmetric bilinear forms and some of their applications. Izv. Akad. Nauk SSSR43, 111–177 (1979), Math. USSR Izvestija14, 103–167 (1980)Google Scholar
  13. 13.
    Oda, T.: A note on the Tate conjecture for K3 surfaces. Proc. Japan. Acad. Ser A56, 296–300 (1980)Google Scholar
  14. 14.
    Okamoto, M.: On a certain decomposition of 2-dimenional cycles on a product of two algebraic surfaces. Proc. Japan Acad. Ser A57, 321–325 (1981)Google Scholar
  15. 15.
    Piateckii-Shapiro, I., Shafarevich, I.R.: A Torelli theorem for algebraic surfaces of type K3. Izv. Akad. Nauk SSSR35, 530–572 (1971); Math. USSR Izvestija5, 547–587 (1971)Google Scholar
  16. 16.
    Shafarevich, I.R., ed.: Algebraic surfaces. Proc. Steklov Institute of Math.75, (1965)Google Scholar
  17. 17.
    Shioda, T.: The period map of abelian surfaces. J. Fac. Sci. Univ. Tokyo25, 47–59 (1978)Google Scholar
  18. 18.
    Shioda, T., Inose, H.: On singular K3 surfaces. Complex analysis and algebraic geometry: papers dedicated to K. Kodaira. Iwanami Shoten and Cambridge University Press 1977, pp. 119–136Google Scholar
  19. 19.
    Siu, Y.-T.: A simple proof of the surjectivity of the period map of K3 surfaces. Manuscripta math.35, 311–321 (1981)Google Scholar
  20. 20.
    Siu, Y.-T.: Every K3 surface is Kähler. Invent. math.73, 139–150 (1983)Google Scholar
  21. 21.
    Todorov, A.: Applications of the Kähler-Einstein-Calabi-Yau metric to moduli of K3 surfaces. Invent. math.61, 251–265 (1980)Google Scholar
  22. 22.
    Wu, W.T.: Classes caractéristiques eti-carrés d'une variété. C.R. Acad. Sci. Paris230, 508 (1950)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • D. R. Morrison
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations