Skip to main content
SpringerLink
Log in

Differential geometry “in the large” of plane algebraic curves and integral formulas for invariants of singularities

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We generalize the Plücker formula for the number of inflection points of a complex projective curve and derive a formula for the number of sextatic points of such a curve. We also obtain an upper estimate for the number of vertices of a real algebraic curve. The proof uses a new result related with integration on the Euler characteristic. Bibliography: 5 titles.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Cartan,Oeuvres Complètes, Gauthier-Villars, Paris (1953).

    Google Scholar 

  2. O. Ya. Viro, “Some integral calculus based on the Euler characteristic,”Lect. Notes Math.,1346, 127–138 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  3. C. T. C. Wall, “Duality of real projective plane curves: Klein’s equation,” Preprint.

  4. W. Blaschke,Einführung in die Differentialgeometrie (1950).

  5. W. Blaschke and H. Reichardt,Einführung in die Differentialgeometrie, 2d ed., Springer-Verlag, Berlin (1960).

    MATH  Google Scholar 

Download references

Authors
  1. A. O. Viro
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 255–268.

Translated by N. Yu. Netsvetaev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Viro, A.O. Differential geometry “in the large” of plane algebraic curves and integral formulas for invariants of singularities. J Math Sci 91, 3499–3507 (1998). https://doi.org/10.1007/BF02434928

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02434928

Keywords

Search

Navigation