Skip to main content

Irreducible Degenerations of Primary Kodaira Surfaces

  • Chapter
Complex Geometry

Abstract

We classify irreducible d-semistable degenerations of primary Kodaira surfaces. As an application we construct a canonical partial completion for the moduli space of primary Kodaira surfaces.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. V. Alexeev, Complete moduli in the presence of semiabelian group action, preprint, 1999.

    Google Scholar 

  2. A. Ash, D. Mumford, M. Rapoport, Y. Tai, Smooth compactifications of locally symmetric varieties. Math. Sci Press, Brookline, 1975.

    Google Scholar 

  3. W. Barth, C. Peters, A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgebiete 4(3) (1984), Springer, Berlin etc.

    Google Scholar 

  4. C. Borcea, Moduli for Kodaira surfaces. Compos. Math. 52 (1984), 373–380.

    MathSciNet  MATH  Google Scholar 

  5. P. Deligne, M. Rapoport, Les schémas de modules de courbes elliptiques, in: P. Deligne, W. Kuyk (eds.), Modular Functions of one Variable II, pp. 143–316. Lect. Notes Math. 349 (1973) Springer, Berlin etc.

    Chapter  Google Scholar 

  6. R. Friedman, Global smoothings of varieties with normal crossings, Ann. Math. 118 (2) (1983), 75–114.

    Article  MATH  Google Scholar 

  7. R. Friedman, N. Shepherd-Barron, Degenerations of Kodaira surfaces, in: R. Friedman, D. Morrison (eds.). The Birational Geometry of Degenerations, pp. 261–275. Prog. Math. 29 (1983), Birkhäuser, Boston etc.

    Google Scholar 

  8. A. Fujiki, On the Douady space of a compact complex space in the category C. II, Publ. Res. Inst. Math. Sci. 20 (1984), 461–489.

    Article  MathSciNet  MATH  Google Scholar 

  9. T. Fujita, Semipositive line bundles, J. Fac. Sci. Univ. Tokyo 30 (1983), 353–378.

    MATH  Google Scholar 

  10. M. Kato, Topology of Hopf surfaces, J. Math. Soc. Japan 27 (1975), 222–238.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Kato, Erratum to “Topology of Hopf surfaces,” J. Math. Soc. Japan 41 (1989), 173–174.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Kodaira, On the structure of compact complex analytic surfaces II, III, Am. J. Math. 88 (1966), 682–721; 90 (1968), 55–83.

    Article  MathSciNet  MATH  Google Scholar 

  13. V. Kulikov, Degenerations of K 3 surfaces and Enriques surfaces, Math. USSR, Izv. 11 (1977), 957–989.

    Article  MATH  Google Scholar 

  14. H. Lange, C. Birkenhake, Complex abelian varieties, Grundlehren Math. Wiss. 302 (1992), Springer, Berlin etc.

    Google Scholar 

  15. D. Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5 (1970), Oxford University Press, London

    Google Scholar 

  16. I. Nakamura, On moduli of stable quasi abelian varieties, Nagoya Math. J. 58 (1975), 149–214.

    MathSciNet  MATH  Google Scholar 

  17. S. Nakano, On the inverse of monoidal transformation, Publ. Res. Inst. Math. Sci., Kyoto Univ. 6 (1971), 483–502.

    Article  MATH  Google Scholar 

  18. K. Nishiguchi, Canonical bundles of analytic surfaces of class VII0, in: H. Hijikata, H. Hironaka et al. (eds.). Algebraic Geometry and Commutative Algebra II, pp. 433–452, Academic Press, Tokyo, 1988.

    Google Scholar 

  19. V. Palamodov, Deformations of complex spaces, Russ. Math. Surveys 31(3) (1976), 129–197.

    Article  MathSciNet  Google Scholar 

  20. U. Persson, On degenerations of algebraic surfaces, Mem. Am. Math. Soc. 189 (1977).

    Google Scholar 

  21. U, Persson, H. Pinkham, Degeneration of surfaces with trivial canonical bundle, Ann. Math. 113(2) (1981), 45–66.

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. 79 (1957), 809–824.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Wehler, Versal deformation of Hopf surfaces. J. Reine Angew. Math. 328 (1981), 22–32.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Schröer, S., Siebert, B. (2002). Irreducible Degenerations of Primary Kodaira Surfaces. In: Bauer, I., Catanese, F., Peternell, T., Kawamata, Y., Siu, YT. (eds) Complex Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56202-0_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-56202-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62790-3

  • Online ISBN: 978-3-642-56202-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics