On Double Planes with Kodaira Dimension Zero

  • A. Calabri
Chapter
Part of the NATO Science Series book series (NAII, volume 36)

Abstract

In this paper we report on a work in progress about the classification of birational equivalence classes of double planes which are surfaces of Kodaira dimension zero, namely K3, Enriques and bielliptic surfaces.

Key words

double planes birational equivalence K3 surfaces Enriques surfaces bielliptic surfaces 

Mathematics Subject Classification (2000)

14J28 14E99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Averbuh, B.C. (1965) Chapter X and Appendix, in LR. Šafarevič et al., Algebraie surfaces, Proc. Steklov Inst. Math. 75.Google Scholar
  2. Bagnera, G., and De Franchis, M. (1908) Le superfieie algebriehe le quali ammettono una rapp-resenta/ione parametrica mediante fun/ioni iperellittiehe di due argomenti, Mem. Soc. Italiana delle Seienzc detta del XL 15. 251–343.Google Scholar
  3. Barth, W., Peters, C., and Van de Ven, A. (1984) Compact complex surfaces, Ergebnisse der Math., 3. Folge, Band 4, Springer, Berlin.MATHCrossRefGoogle Scholar
  4. Bayle, L., and Beauville, A. (2000) Birational involutions of P2, Asian J. Math. 4, no. 1, 1 1–17.MathSciNetGoogle Scholar
  5. Calabri, A. (2000) On rational and ruled double planes, preprint, submitted.Google Scholar
  6. Calabri, A., and Ferraro, R. (2000) Explicit resolution of double point singularities of surfaces, preprint, submitted.Google Scholar
  7. Casas-Alvero. E. (2000) Singularities of plane curves, London Math. Soc. Lect. Note Series 276, Cambridge University Press, Cambridge.MATHCrossRefGoogle Scholar
  8. Castelnuovo, G., and Enriques, F. (1900) Sulle condizioni di razionalità dei piani doppi, Rend. Circ. Mat. Palermo 14, 290–302.MATHCrossRefGoogle Scholar
  9. Ciliberto, C, and Pareschi. G. (1995) Pencils of minimal degree on curves on a K3 surface, J. reine angew. Math. 460, 15–36.MathSciNetMATHGoogle Scholar
  10. De Franchis, M. (1904) I piani doppi dotati di due o piu differenziali totali di prima specie, Rend. Accad. Lincei 13, 688–695.MATHGoogle Scholar
  11. Enriques, F. (1896) Sui piani doppi di genere uno, Mem. Soc. Italiana delle Scienze detta dei XL 10, 201–224.Google Scholar
  12. Enriques, F. (1906) Sopra le superficie algebriehe di bigenere uno, Mem. Soc. Italiana delie Scienze detta dei XL 14.Google Scholar
  13. Enriques, F.. and Chisini, O. (1920) Lezioni sulla teoria geometrica delie equazioni e delle funzioni algehriche, 5 voll., Zaniehelli.Google Scholar
  14. Laufer, H. (1978) On normal two-dimensional double point singularities, Israel J. Math. 31, 315–334.MathSciNetMATHCrossRefGoogle Scholar
  15. Saint-Donat, B. (1974) Projective models of K-3 surfaces, Amer. J. Math. 96, 602–639.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • A. Calabri
    • 1
  1. 1.University of Rome “Tor Vergata”Italy

Personalised recommendations