Skip to main content

Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface

  • Chapter
Book cover Number Fields and Function Fields—Two Parallel Worlds

Part of the book series: Progress in Mathematics ((PM,volume 239))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Y. Arakelov, An intersection theory for divisors on an arithmetic surface, Izv. Akad. Nauk., 38 (1974), 1179–1192; cf. Math. USSR Izv., 8 (1974), 1167–1180.

    MATH  MathSciNet  Google Scholar 

  2. H. F. Baker, On the hyperelliptic sigma functions, Amer. J. Math., 20 (1898), 301–384.

    Article  MATH  MathSciNet  Google Scholar 

  3. J.-B. Bost, Fonctions de Green-Arakelov, fonctions thêta et courbes de genre 2, C. R. Acad. Sci. Paris Ser. I, 305 (1987), 643–646.

    MATH  MathSciNet  Google Scholar 

  4. V. M. Buchstaber, V. Z. Enolskii, and D. V. Leykin, Kleinian functions, hyperelliptic jacobians and applications, Rev. Math. Math. Phys., 10 (1997), 1–125.

    Google Scholar 

  5. V. M. Buchstaber, V. Z. Enolskii, and D.V. Leykin, Rational analogs of abelian functions, Functional Anal. Appl., 33-2 (1999), 83–94.

    Article  MATH  Google Scholar 

  6. V. M. Buchstaber, D. V. Leykin, and V. Z. Enolskii, σ-functions of (n, s)-curves, Russian Math. Surveys, 54 (1999), 628–629.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. Faltings, Calculus on arithmetic surfaces, Ann. Math., 119 (1984), 387–424.

    Article  MATH  MathSciNet  Google Scholar 

  8. W. Fulton and J. Harris, Representation Theory: A First Course, Graduate Texts in Mathematics 129, Springer-Verlag, New York, 1991.

    Google Scholar 

  9. D. Grant, A generalization of Jacobi’s derivative formula to dimension two, J. Reine Angew. Math., 392 (1988), 125–136.

    MATH  MathSciNet  Google Scholar 

  10. R. de Jong, Arakelov invariants of Riemann surfaces, preprint, submitted.

    Google Scholar 

  11. R. de Jong, Explicit Mumford Isomorphism for Hyperelliptic Curves, Prépublication M/04/51, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France, 2004; submitted.

    Google Scholar 

  12. Y. Ônishi, Determinant expressions for hyperelliptic functions (with an appendix by Shigeki Matsutani), preprint.

    Google Scholar 

  13. P. Lockhart, On the discriminant of a hyperelliptic curve, Trans. Amer. Math. Soc., 342-2 (1994), 729–752.

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Mumford, Tata Lectures on Theta I, II, Progress in Mathematics 28, 43, Birkhäuser Boston, Cambridge, MA, 1984.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Boston

About this chapter

Cite this chapter

de Jong, R. (2005). Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface. In: van der Geer, G., Moonen, B., Schoof, R. (eds) Number Fields and Function Fields—Two Parallel Worlds. Progress in Mathematics, vol 239. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4447-4_10

Download citation

Publish with us

Policies and ethics