Skip to main content
SpringerLink
Log in

Compactifications of the period space of Enriques surfaces Part I

  • Published:
Mathematische Zeitschrift 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. Baily, W.L. Jr., Borel, A.: Compactification of arithmetic quotients of bounded symmetric domains. Ann. Math.84, 442–528 (1966)

    Article  MathSciNet  Google Scholar 

  2. Barth, W., Peters, C.: Automorphisms of Enriques surfaces. Invent. Math.73, 383–411 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  3. Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces, Berlin Heidelberg New York: Springer 1984

    MATH  Google Scholar 

  4. Borel, A.: Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem. J. Differ. Geom.6, 543–560 (1972)

    MATH  MathSciNet  Google Scholar 

  5. Cartan, H.: Quotient d'un espace analytique par un groupe d'automorphismes. In: Symposium in Honor of S. Lefschetz. Princeton: Princeton University Press 1957

    Google Scholar 

  6. Clemens, C.H.: Degenerations of Kähler manifolds. Duke Math. J.44, 215–290 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cossec, F.: On the Picard groups of Enriques surfaces. Math. Ann.271, 577–600 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dolgachev, I.: On automorphisms of Enriques surfaces. Invent. Math.76, 163–177 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Friedman, R.: Hodge theory, degenerations, and the global Torelli problem. Ph.D. thesis, Harvard University 1981

  10. Friedman, R.: A new proof of the global Torelli theorem forK3 surfaces. Ann. Math.120, 237–296 (1984)

    Article  Google Scholar 

  11. Horikawa, E.: On the periods of Enriques surfaces I, Math. Ann.234, 73–88 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  12. Horikawa E.: On the periods of Enriques surfaces II, Math. Ann.235, 217–246 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kulikov, V.: Degenerations ofK3 surfaces and Enriques surfaces, Math. USSR Isv.11, 957–989 (1977)

    Article  MATH  Google Scholar 

  14. Looijenga, E.: Semi-toric partial compactifications. Report 8520 (1985), Department of Mathematics, Catholic University Nijmegen, The Netherlands

    Google Scholar 

  15. Looijenga, E.: New compactifications of locally symmetric varieties In: Proceedings of the 1984 Vancouver conference in algebraic geometry. (C.M.S. Conference Proceedings vol. 6, pp. 341–364) Providence, Rhode Island: Am. Math. Soc. 1986

    Google Scholar 

  16. Mumford, D., Fogarty, J.: Geometric invariant theory (2nd edition) Berlin Heidelberg New York: Springer 1982

    MATH  Google Scholar 

  17. Namikawa, Y.: Periods of Enriques surfaces. Math. Ann.270, 201–222 (1985)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  19. Nikulin, V.: Finite automorphism groups of KählerK3 surfaces. Trans Moscow Math. Soc.38, 71–135 (1980)

    Google Scholar 

  20. Persson, U., Pinkham, H.: Degenerations of surfaces with trivial canonical bundle. Ann. Math.113, 45–66 (1981)

    Article  MathSciNet  Google Scholar 

  21. Satake, I.: On the compactifications of the Siegel space. J. Indian Math. Soc.20, 259–281 (1956)

    MathSciNet  Google Scholar 

  22. Satake, I.: On compactifications of quotient spaces for arithmetically discontinuous groups. Ann. Math.72, 555–580 (1960)

    Article  MathSciNet  Google Scholar 

  23. Scattone, F.: On the compactification of moduli spaces for algebraicK3 surfaces. Ph.D. thesis, Columbia University 1984

  24. Shah, J.: Projective degenerations of Enriques surfaces. Math. Ann.256, 475–495 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  25. Sterk, H.: Compactifications of the period space of Enriques surfaces. Arithmetic and geometric aspects. Ph.D. thesis, Katholieke Unitersiteit Nijmegen, The Netherlands 1988

    Google Scholar 

  26. Vinberg, E.B.: Some arithmetical discrete groups in Lobachevskii spaces. In: Proc. Int. Coll on Discrete Subgroups of Lie Groups and Appl. to Moduli (Tata Institute of Fundamental Research Studies in Mathematics, Vol. 7, pp. 323–348) Oxford: Oxford University Press 1975

    Google Scholar 

  27. Vinberg, É.B.: The two most algebraicK3 surfaces. Math. Ann.265, 1–21 (1983)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Author notes

  1. Hans Sterk

    Present address: Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Moidergracht 24, NL-1018 TV, Amsterdam, The netherlands

Authors and Affiliations

  1. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    Hans Sterk

Authors
  1. Hans Sterk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Netherlands Organization for Scientific Research (NWO)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sterk, H. Compactifications of the period space of Enriques surfaces Part I. Math Z 207, 1–36 (1991). https://doi.org/10.1007/BF02571372

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571372

Keywords

Search

Navigation