Skip to main content
SpringerLink
Log in

Strebel differentials on families of hyperelliptic curves

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

Abstract

Our paper is devoted to Strebel pairs on families of hyperelliptic curves. We provide a complete proof of the fact that the constructed differentials are Strebel and point out the connections between the introduced constructions and classical objects of complex algebraic geometry.

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. N. Ya. Amburg, “The example of the regular Strebel differential,” Usp. Mat. Nauk, 57, No. 5, 149 (2002).

    MathSciNet  Google Scholar 

  2. I. V. Artamkin, Yu. A. Levitskaya, and G. B. Shabat, “Examples of families of Strebel differentials on the hyperelliptic curves,” to appear.

  3. A. Douady and J. Hubbard, “On the density of Strebel differentials,” Invent. Math., 30, 175–179 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  4. Ph. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley–Interscience (1994).

  5. G. B. Shabat, “Complex analysis and dessins,” in: Complex Analysis in Modern Science [in Russian], Mir, Moscow (2001), pp. 253–264.

    Google Scholar 

  6. I. R. Shafarevich, Fundamentals of Algebraic Geometry [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  7. K. Strebel, Quadratic Differentials, Springer (1984).

Download references

Author information

Authors and Affiliations

  1. Moscow State Institute of Radioengineering, Electronics and Automation, Moscow, Russia

    I. V. Artamkin

  2. Moscow State University, Moscow, Russia

    Yu. A. Levitskaya

  3. Russian State University for the Humanities, Moscow, Russia

    G. B. Shabat

Authors
  1. I. V. Artamkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Levitskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. B. Shabat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Artamkin.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 121–130, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Artamkin, I.V., Levitskaya, Y.A. & Shabat, G.B. Strebel differentials on families of hyperelliptic curves. J Math Sci 158, 87–93 (2009). https://doi.org/10.1007/s10958-009-9377-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-009-9377-3

Keywords

Search

Navigation