Skip to main content

Geometrical aspects of the Kadomtsev-Petviashvili equation

  • Conference paper
  • First Online:
Global Geometry and Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1451))

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 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight 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. L. Alvarez-Gaumé, C. Gomez, C. Reina, Loop groups, Grassmannians and string theory, Phys. Lett. B, 190 (1987), 55–62.

    Article  MathSciNet  Google Scholar 

  2. E. Arbarello, Fay's trisecant formula and a characterisation of Jacobian Varieties, Proceedings of Symposia in Pure Mathematics Vol. 46 (1987).

    Google Scholar 

  3. E. Arbarello, M. Cornalba, P.A. Griffiths, J. Harris, Geometry of algebraic curves, Vol. I Berlin, Heidelberg, New York: Springer 1985, Vol. II (to appear).

    Book  MATH  Google Scholar 

  4. E. Arbarello and C. De Concini, On a set of equations characterizing Riemann matrices, Ann. of Math. (2) 120 (1984), 119–140.

    Article  MathSciNet  MATH  Google Scholar 

  5. E. Arbarello, C. De Concini, Another proof of a conjecture of S. P. Novikov on periods and abelian integrals on Riemann surfaces, Duke Math. J., 54 (1987), 163–178.

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Arbarello, C. De Concini,, V. Kac, C. Procesi, Moduli spaces of curves and representation theory, Comm. Math. Phys, 114 (1988).

    Google Scholar 

  7. A. Beauville and O. Debarre, Une rélation entre deux approches du problème de Schottky, Preprint.

    Google Scholar 

  8. A.A. Beilinson, Ju.L. Manin, The Mumford form and the Polyakov measure in string theory,comm. Mathy. Phys., 107 (1986), 359–376.

    Article  MathSciNet  MATH  Google Scholar 

  9. A.A. Beilinson, Yu.L. Manin, V.V. Schectman, Sheaves of the Virasoro and Neveu-Schwarz algebras, Moscow University preprint, 1987.

    Google Scholar 

  10. M. Cornalba, Complex Tori and Jacobians in Complex Analysis and its applications, Vol. II IAEA-SMR 18/24, Vienna 1976.

    Google Scholar 

  11. E. Date, M. Jimbo, M. Kashiwara, T. Miwa, Transformation groups for soliton equation, in: Noalinear Integrabic Systems Classical Theory and Quantum Theory, World Scientific, Singapore, 1983, 39–119.

    Google Scholar 

  12. R. Donagi, The Schottky Problem, in E. Sernesi, Theory of Moduli, Lecture Notes Vol. 1337 Springer-Verlag, Berlin-New York 1985.

    Google Scholar 

  13. B.A. Dubrovin, Theta functions and non-linear equations, Russian Math. Surveys, 36, 2 (1981), 11–92.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Fay, Theta Functions on Riemann Surfaces, Lecture Notes, Vol. 352, Springer-Verlag, Berlin-New York, 1973.

    MATH  Google Scholar 

  15. H.M. Farkas, On Fay's trisecant formula, J. Analyse Math. 44 (1984), 205–217.

    Article  MathSciNet  Google Scholar 

  16. H. Farkas, H. Rauch, Period relations of Schottky type on Riemann surfaces, Ann. Math., 62 (1970), 434–461.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. C. Gunning, Some curves in Abelian varieties, Invent. Math., 66 (1982), 377–389.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Harer, The second homology group of the mappings class group of an orientable surface, Invent. Math., 72 (1983), 221–239.

    Article  MathSciNet  MATH  Google Scholar 

  19. I.M. Krichever, Methods of Algebraic Geometry in the theory of nonlinear equations, Russian Math. Surveys, 32 (1977), 185–213.

    Article  MathSciNet  MATH  Google Scholar 

  20. V.G. Kac, D.H. Peterson, Spin and wedge representations of infinite dimensional Lie algebras and groups, Proc. Nat. Acad. Sci. U.S.A., 78 (1981), 3308–3312.

    Article  MathSciNet  MATH  Google Scholar 

  21. N. Kawamoto, Y. Namikawa, A. Tsuchiva, Y. Yamada, Geometric realization of conformal field theory on Riemann surfaces, Comm. Math. Phys. (in press).

    Google Scholar 

  22. J. Igusa, Theta Functions, Grundlehren der Math. Wiss., 194, Springer, 1972.

    Google Scholar 

  23. Yu. Manin, Quantum string theory and algebraic curvers, Berkeley J.C.M. Talk, 1986.

    Google Scholar 

  24. D. Mumford, Curves and their Jacobians, Ann. Arbor, University of Michigan Press, 1975.

    MATH  Google Scholar 

  25. D. Mumford, An enumerative geometry of the moduli space, in Arithmetic and Geometry, papers dedicated to I.R. Shafarevich, Birkhaser, Boston, 1983.

    Google Scholar 

  26. D. Mumford, An Algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related non-linear equations, (Proc. Internat. Sympos. Alg. Geometry, Kyoto, 1977), Kinokuniy Book Store, Tokyo, 1978, 115–153.

    Google Scholar 

  27. D. Mumford, Tata lectures on theta. II, Birkhaüser, Boston, 1983.

    Book  MATH  Google Scholar 

  28. D. Mumford, J. Fogarty, Geometric invariant theory, Ergebnisse der Math., 34, Springer.

    Google Scholar 

  29. M. Mulase, Cohomological structure in soliton equations and Jacobian varieties, J. Differential Geom., 19 (1984), 403–430.

    MathSciNet  MATH  Google Scholar 

  30. S.P. Novikov, The periodic problem for the Korteweg-de Vries equation, Functional Anal. Appl. 8 (1974), 236–246.

    Article  MathSciNet  MATH  Google Scholar 

  31. F. Oort, J. Steenbrink, The local Torelli problem for algebraic curves, Journées de Géometrie Algébrique d'Angers, juillet 1979, 157–204, Sijthoff and Noordhoff, Alphen aan den Rijn, 1980.

    Google Scholar 

  32. A. Pressley, G. Segal, Loop Groups, Oxford University press, 1986.

    Google Scholar 

  33. A.K. Raina, Fay's trisecant identity and conformal field theory, preprint TIFR/TH/88-37.

    Google Scholar 

  34. G. Segal, G. Wilson, Loop groups and equations of KdV type, Publ. Math., K.E.S. 61.

    Google Scholar 

  35. T. Shiota, Characterization of Jacobian varieties in terms of soliton equations, Invent. Math., 83 (1986), 333–382.

    Article  MathSciNet  MATH  Google Scholar 

  36. B. Van Geemen, The Schottky problem and moduli spaces of Kummer varieties, U. of Urecht thesis, 1985.

    Google Scholar 

  37. W. Wirtinger, Untersuchungen über Thetafunctionen, Teubner, Berlin, 1985.

    MATH  Google Scholar 

  38. G. Welters, A criterion for Jacobi varieties, Ann. Math. 120 (1984), 497–504.

    Article  MathSciNet  MATH  Google Scholar 

  39. G. Welters, On flexes of the Kummer variety, Nederl. Akad. Wetensch. Proc. Ser. A 86 45 (1983), 501–520.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Mauro Francaviglia Francesco Gherardelli

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Arbarello, E., De Concini, C. (1990). Geometrical aspects of the Kadomtsev-Petviashvili equation. In: Francaviglia, M., Gherardelli, F. (eds) Global Geometry and Mathematical Physics. Lecture Notes in Mathematics, vol 1451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085066

Download citation

  • DOI: https://doi.org/10.1007/BFb0085066

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53286-6

  • Online ISBN: 978-3-540-46813-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics