Skip to main content

Reider-serrano's method on normal surfaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1417)

Keywords

  • Effective Divisor
  • Cartier Divisor
  • Birational Morphism
  • Fundamental Cycle
  • Exceptional Curve

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andreatta,M., Sommese,A.:On the adjunction mapping for singular projective varieties. Preprint

    Google Scholar 

  2. Artin, M.:On isolated rational singularities of surfaces. Amer. J. Math. 88, 129–136 (1966)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Beltrametti,M., Francia,P., Sommese,A.:On Reider's method and higher order embeddings. Preprint

    Google Scholar 

  4. Beltrametti, M., Lanteri, A.:On the 2 and 3-connectedness of ample divisors on a surface. Manuscripta Math. 58, 109–128 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Bombieri, E.: Canonical models of surfaces of general type. Publ. Math. IHES 42, 172–219 (1973)

    CrossRef  MathSciNet  Google Scholar 

  6. Fujita,T.: Remarks on adjoint bundles of polarized surfaces. Preprint

    Google Scholar 

  7. Ionescu,P.:Ample and very ample divisors. Preprint

    Google Scholar 

  8. Laufer, H.:On minimally elliptic singularities. Amer.J.Math. 99, 1257–1295 (1977)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Laufer, H.:Weak simultaneous resolution for deformations of Gorenstein surface singularities. Proc. Symp. Pure Math. 40, 1–29 (1983)

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Laufer, H.:Generation of 4-pluricanonical forms for surface singularities. Amer.J.Math. 109, 571–590 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Miyaoka,Y.:On the Mumford-Ramanujam vanishing theorem on a surface. In:Journées de Géom. Alg. d'Angers, pp. 239–247. Sijthoff and Noordhoff, 1980

    Google Scholar 

  12. Morrow, J., Rossi, H.:Canonical embeddings. Trans. A.M.S. 261, 547–565 (1980)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Mumford,D.:Some footnotes to the work of C.P. Ramanujam. In: C.P.Ramanujam-a tribute, pp. 247–262, Springer-Verlag, 1978

    Google Scholar 

  14. Ramanujam, C.P.:Remarks on the Kodaira vanishing theorem. J. Indian Math. Soc. 36, 41–51 (1972)

    MathSciNet  MATH  Google Scholar 

  15. Reid,M.:Elliptic Gorenstein singularities of surfaces. Preprint (1975)

    Google Scholar 

  16. Reider, I.:Vector bundles of rank 2 and linear systems on algebraic surfaces. Ann. Math. 127, 309–316 (1988)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Sakai, F.:Enriques classification of normal Gorenstein surfaces. Amer.J.Math. 104, 1233–1341 (1982)

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Sakai, F.:Anticanonical models of rational surfaces. Math. Ann. 269, 389–410 (1984)

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Sakai, F.:Weil divisors on normal surfaces. Duke Math. J. 51, 877–887 (1984)

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Serrano, F.:Extension of morphisms defined on a divisor. Math. Ann. 277, 395–413 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. Shepherd-Barron,N.I.:Some questions on singularities in 2 and 3 dimensions. Thesis, Univ.of Warwick, 1980

    Google Scholar 

  22. Sommese, A., Van de Ven, A.:On the adjunction mapping. Math.Ann. 278, 593–603 (1987)

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Prof. Dr. F.Hirzebruch on his 60th birthday

Rights and permissions

Reprints and Permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Sakai, F. (1990). Reider-serrano's method on normal surfaces. In: Sommese, A.J., Biancofiore, A., Livorni, E.L. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 1417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083346

Download citation

  • DOI: https://doi.org/10.1007/BFb0083346

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52217-1

  • Online ISBN: 978-3-540-46934-6

  • eBook Packages: Springer Book Archive