Skip to main content
Log in

The maximal number of quotient singularities on surfaces with given numerical invariants

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [Ba] Basset, A.B.: The maximum number of double points on a surface. Nature73, 246 (1906)

    Google Scholar 

  • [Be] Beauville, A.: Sur le nombre maximum de points double d'une surface dansP 3 (μ(5)=31). Géométrie algébrique d'Anger 1979, pp. 207–215. Alphen an den Rijn: Sijthoff & Nordohoff 1980

    Google Scholar 

  • [Br] Bruce, J.W.: An upper bound for the number of singularities on a projective hypersurface. Bull. Lond. Math. Soc.13, 47–51 (1981)

    Google Scholar 

  • [CC] Catanese, F., Ceresa, G.: Constructing sextic surfaces with a given number of nodes. J. Pure Appl. Algebra23, 1–12 (1982)

    Google Scholar 

  • [G] Gallarati, D.: Una superficie dell'ottavo ordine con 160 nodi. Acc. Ligure Sci. Lett.14, 1–7 (1957)

    Google Scholar 

  • [Ka] Kawamata, Y.: On the classification of non-complete algebraic surfaces. Lecture Note in Mathematics, Vol. 732, pp. 215–232. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  • [Kr] Kreiss, H.O.: Über syzygetische Flächen. Ann. Math.41, 105–111 (1955)

    Google Scholar 

  • [M] Miyaoka, Y.: On the Chern numbers of surfaces of general type. Invert. Math.42, 225–237 (1977)

    Google Scholar 

  • [N] Nikulin, V.V.: On Kummer surfaces. Math. USSR Izv.9, 261–275 (1975)

    Google Scholar 

  • [Sa 1] Sakai, F.: Semi-stable curves on algebraic surfaces and logarithmic pluri-canonical maps. Math. Ann.254, 89–120 (1980)

    Google Scholar 

  • [Sa2] Sakai, F.: Curves with trivial dualizing sheaf on algebraic surfaces. Am. J. Math.104, 1217–1231 (1982)

    Google Scholar 

  • [Se1] Segre, B.: Sur massimo numero di nodi delle superficie di dato ordine. Bull. U.M.I.2, 204–212 (1947)

    Google Scholar 

  • [Se2] Segre, B.: On arithmetical properties of quartic surfaces. Proc. London Math. Soc. 2nd Ser.49, 353–395 (1947)

    Google Scholar 

  • [St1] Stagnaro, E.: Sul massimo numero di punti doppi isolati di una superficie algebrica diP 3. Rend. Sem. Nat. Padva59, 179–198 (1978)

    Google Scholar 

  • [St2] Stagnaro, E.: On the Basset limitations for the maximum number of isolated singularities on an algebraic surface. Proc. of the Trento Conference, pp. 291–304. New York, Basel: Decker 1983

    Google Scholar 

  • [Y] Yau, S.T.: Calabi's conjecture and some new results in algebraic geometry. Proc. Nat. Acad. Sci. USA74, 1798–1799 (1977)

    Google Scholar 

  • [Z] Zariski, O.: The theorem of Rimann-Roch for high multiple of an effective divisor on a surface. Ann. Math.76, 506–615 (1962)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by Mathematical Research Centre, University of Warwick

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miyaoka, Y. The maximal number of quotient singularities on surfaces with given numerical invariants. Math. Ann. 268, 159–171 (1984). https://doi.org/10.1007/BF01456083

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01456083

Keywords

Navigation