Skip to main content
SpringerLink
Log in

Classification of non-rigid families of K3 surfaces and a finiteness theorem of Arakelov type

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Arakelov, A.: Families of algebraic curves with fixed degeneracies. (English transl.), Math. USSR Izv.5, 1277–1302 (1971)

    Google Scholar 

  2. Burns, D., Rapoport, M.: On the Torelli problem for Kählerian K3 surfaces. Ann. Sci. Ecole Norm. Super.8, 233–274 (1975)

    Google Scholar 

  3. Deligne, P.: Théorie de Hodge, II. Publ. Math. IHES40, 5–57 (1971)

    Google Scholar 

  4. Deligne, P.: La conjecture de Weil pour les surfaces K3. Invent. Math.15, 206–226 (1972)

    Google Scholar 

  5. Faltings, G.: Arakelov's theorem for Abelian varieties. Invent. Math.73, 337–347 (1983)

    Google Scholar 

  6. Kuga, M.: Fiber varieties over a symmetric space whose fibers are abelian varieties, I, II. Lect. Notes, Univ. Chicago, 1963–1964

  7. Kulikov, V.: Surjectivity of the period mapping for surfaces of type K3, (in Russian), Usp. Mat. Nauk.32, 4, 257–258 (1977)

    Google Scholar 

  8. Morrison, D.R.: Some remarks on the moduli of K3 surfaces. Classification of algebraic and analytis manifolds. Ueno, K. (ed.). Prog. Math.39, 303–332 (1983)

    Google Scholar 

  9. Morrison, D.R.: On the moduli of Todorov surfaces. Algebraic geometry and commutative algebra, in honor of Masayoshi Nagata, 313–355. Kinokuniya (1988)

  10. Nikulin, V.: Integral symmetric bilinear forms and some of their applications. Math. USSR Izv.14, 103–167 (1980)

    Google Scholar 

  11. Noguchi, J.: Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces. Invent. Math.93, 15–34 (1988)

    Google Scholar 

  12. Peters, C.: Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems, Comp. Math.75, 113–126 (1990)

    Google Scholar 

  13. Satake, I.: Algebraic structures of symmetric domains, Publ. of the Math. Soc. of Japan,14, Iwanami Shoten and Princeton University Press 1980

  14. Schmid, W.: Variation of Hodge structure: the singularities of the period mapping. Invent. Math.22, 211–320 (1973)

    Google Scholar 

  15. Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Publ. of the Math. Soc. of Japan,11, Iwanami Shoten and Princeton University Press 1971

  16. Zarhin, Yu.G.: Hodge groups of K3 surfaces. J. Reine Angew. Math.341, 193–220 (1983)

    Google Scholar 

  17. Zarhin, Yu.G.: Weights of simple Lie algebras in the cohomology of algebraic varieties. (English transl.) Math. USSR Izv.24, 241–281 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Hokkaido University, 060, Sapporo, Japan

    Masa-Hiko Saito

  2. Department of Mathematics, Johns Hopkins University, 21218, Baltimore, MD, USA

    Steven Zucker

Authors
  1. Masa-Hiko Saito
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven Zucker
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by the National Science Foundation, through Grant DMS-8800355

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saito, MH., Zucker, S. Classification of non-rigid families of K3 surfaces and a finiteness theorem of Arakelov type. Math. Ann. 289, 1–31 (1991). https://doi.org/10.1007/BF01446555

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01446555

Keywords

Search

Navigation