Skip to main content

Enumeration of Rational Curves Via Torus Actions

  • Conference paper

Part of the book series: Progress in Mathematics ((PM,volume 129))

Abstract

This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   249.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. S. Aspinwall, D. R. Morrison, Topological field theory and rational curves, Commun. Math. Phys. 151 (1993), 245–262.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Baum, W. Fulton, R. MacPherson, Riemann-Roch for singular varieties, Publ. Math. I. H. E. S. 45 (1975), 101–145.

    MathSciNet  MATH  Google Scholar 

  3. R. Bott, A residue formula for holomorphic vector fields, Jour. Diff. Geom. 1 (1967), 311–330.

    Google Scholar 

  4. P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus, Publ. Math. I. H. E. S. 36 (1969), 75–110.

    MathSciNet  MATH  Google Scholar 

  5. A. Givental, B. Kim, Quantum cohomology of flag manifolds and Toda lattices, preprint (1993).

    Google Scholar 

  6. C. Itzykson, J.-M. Drouffe, Statistical field theory, Cambridge University Press, 1989.

    Google Scholar 

  7. M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys. 147 (1992), 1–23.

    Article  Google Scholar 

  8. M. Kontsevich, Yu. Manin, Gromov-Witten classes, quantum cohomology and enumerative geometry, MPI preprint and hep-th/9402147 (1994).

    Google Scholar 

  9. M] Yu. Manin, Generating functions in algebraic geometry and sums over trees, this volume.

    Google Scholar 

  10. P. Pansu, Chapter VIII, Compactness, Holomorphic curves in symplectic geometry, eds. M. Audin, J. Lafontaine, Progress in Mathematics, vol. 117, Birkhauser, 1994.

    Google Scholar 

  11. Z. Ran, Enumerative geometry of singular plane curves, Invent. Math. 97 (1989), 447–465.

    MATH  Google Scholar 

  12. Y. Ruan, G. Tian, Mathematical theory of quantum cohomology, preprint (1993).

    Google Scholar 

  13. E. Witten, Two-dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geom. 1 (1991), 243–310.

    Google Scholar 

  14. S. T. Yau, ed., Essays on Mirror Manifolds, International Press Co., Hong Kong, 1992.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Birkhäuser Boston

About this paper

Cite this paper

Kontsevich, M. (1995). Enumeration of Rational Curves Via Torus Actions. In: Dijkgraaf, R.H., Faber, C.F., van der Geer, G.B.M. (eds) The Moduli Space of Curves. Progress in Mathematics, vol 129. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4264-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4264-2_12

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8714-8

  • Online ISBN: 978-1-4612-4264-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics