Skip to main content
SpringerLink
Log in

Moduli Spaces for Special Surfaces of General Type

  • Chapter
Algebraic Geometry and its Applications

Abstract

Classification of algebraic varieties consists of two parts: First find a set of discrete invariants like dimensions, genera, … to describe the basic topological properties of the variety, and then try to make the set of all varieties with given discrete invariants into an algebraic variety, the so called moduli space. The prototypical example is classification of Riemann surfaces: The genus is sufficient to fix the topological (and even differentiable) structure, and the set of all Riemann surfaces of a given genus can be made into an irreducible quasi-projective variety; its dimension is 3g — 3 for g ≥ 2.

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

Access this chapter

Log in via an institution
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

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.

References

  1. Artin, M., Algebraic Construction of Brieskorn’s Resolution, J. Algebra, r 29, 1974, pp. 330–348.

    Article  MathSciNet  MATH  Google Scholar 

  2. Brieskorn, E., Die Auflösung der Rationalen Singularitäten Holomorpher Abbildungen, Math. Ann., 178, 1968, pp. 255–270.

    Article  MathSciNet  MATH  Google Scholar 

  3. Burns, D. M., J. M. Wahl, Local Contributions to Global Deformations of Surfaces, Inv. Math., 26, 1974, pp. 67–88.

    Article  MathSciNet  MATH  Google Scholar 

  4. Catanese, F., On the Moduli Spaces of Surfaces of General Type, J. Diff. Geom., 19, 1984, pp. 483–515.

    MathSciNet  MATH  Google Scholar 

  5. Catanese, F., Moduli and Classification of Irregular Kaehler Manifolds and Algebraic Varieties With Albanese General Type Fibrations, preprint 1990.

    Google Scholar 

  6. Deligne, R, D. Mumford, The Irreducibility of the Space of Curves of a Given Genus, Publ. Math. IHES, 36, (1969), pp. 75–110.

    Article  MathSciNet  MATH  Google Scholar 

  7. Fujita, T., On Kahler Fiber Spaces Over Curves, J. Math. Soc., 30, 1978, pp. 779–794.

    MATH  Google Scholar 

  8. Gieseker, D., Global Moduli for Surfaces of General Type, Inv. Math., 43, 1977, pp. 233–282.

    Article  MathSciNet  MATH  Google Scholar 

  9. Hartshorne, R., Algebraic Geometry, Springer, 1977.

    MATH  Google Scholar 

  10. Horikawa, E., Algebraic Surfaces of General Type With Small c1: 2, I: Ann. Math., 104, 1976, pp. 357–387.

    Article  MathSciNet  MATH  Google Scholar 

  11. Horikawa, E., Algebraic Surfaces of General Type With Small c1: 2, II: Inv. Math., 37, 1976, pp. 121–155.

    Article  MathSciNet  MATH  Google Scholar 

  12. Horikawa, E., Algebraic Surfaces of General Type With Small c1: 2, III: Inv. Math., 47, 1978, pp. 209–248.

    Article  MathSciNet  MATH  Google Scholar 

  13. Horikawa, E., Algebraic Surfaces of General Type With Small c1: 2, IV: Inv. Math., 50, 1979, pp. 103–128.

    Article  MathSciNet  MATH  Google Scholar 

  14. Horikawa, E., Algebraic Surfaces of General Type With Small c1: 2, V: J. Fac. Sci. Univ. Tokyo, Sect. A. Math. 283, 1981, pp. 745–755.

    Google Scholar 

  15. Iitaka, S., Deformations of Compact Complex Surfaces II, J. Math. Soc. Japan, 22, 1970, pp. 247–261.

    Article  MathSciNet  MATH  Google Scholar 

  16. Kas, A., Ordinary Double Points and Obstructed Surfaces, Topology, 16, 1977, pp. 51–64.

    Article  MathSciNet  MATH  Google Scholar 

  17. Maruyama, M., On Classification of Ruled Surfaces, Tokyo, 1970.

    MATH  Google Scholar 

  18. Matsumura, H., On Algebraic Groups of Birational Transformations, Atti Acad. Naz. Lincei, Rend. CI. Sci. Fis. Mat. Natur., 8, 1963, pp. 151–155.

    MathSciNet  Google Scholar 

  19. Morrow J., K. Kodaira, Complex Manifolds, New York, 1971.

    MATH  Google Scholar 

  20. Persson, U., On Chern Invariants of Surfaces of General Type,Comp. Math., 43, 1981, pp. 3–58.

    MathSciNet  MATH  Google Scholar 

  21. Persson, U., An Introduction to the Geography of Surfaces of General Type, Proc. Symp. Pure Math., 46, 1987, pp. 195–218.

    MathSciNet  Google Scholar 

  22. Reid, M., π1 for Surfaces With Small c 1: 2, in Algebraic Geometry Copenhagen Lecture Notes in Mathematics, 732, 1979, pp. 534–544.

    Google Scholar 

  23. Seshadri, C.S., Moduli of π-Vector Bundles Over an Algebraic Curve, in Questions on Algebraic Varieties, C. I. M. E. Lecture Notes, 51, Firenze 1970, pp. 139–260.

    Google Scholar 

  24. Seiler, W.K., Modulräume von Flächen Allgemeinen Typs Mit Einer Faserung Durch Kurven vom Geschlecht zwei, submitted as Habilitationsschrift, Dept. of Mathematics, Universität Mannheim.

    Google Scholar 

  25. Siu, Y.T., Strong Rigidity for Kaehler Manifolds and the Construction of Bounded Holomorphic Functions, in (R. Howe, ed.), Discrete Groups in Analysis Birkhäuser, 1987, pp. 124–151.

    Google Scholar 

  26. Suwa, T., On Ruled Surfaces of Genus 1, J. Math. Soc. Japan, 21, 1969, pp. 291–311.

    Article  MathSciNet  MATH  Google Scholar 

  27. Xiao Gang, Surfaces Fibrees en Courbes de Genre Deux, Lecture Notes in Mathematics 1137, Springer 1985.

    MATH  Google Scholar 

Download references

Authors
  1. Wolfgang K. Seiler
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Purdue University, 47907, West Lafayette, IN, USA

    Chandrajit L. Bajaj

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Seiler, W.K. (1994). Moduli Spaces for Special Surfaces of General Type. In: Bajaj, C.L. (eds) Algebraic Geometry and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2628-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2628-4_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7614-2

  • Online ISBN: 978-1-4612-2628-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation