Skip to main content

Moduli Spaces and Grassmannian

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We calculate the homomorphism of the cohomology induced by the Krichever map of moduli spaces of curves into infinite-dimensional Grassmannian. This calculation can be used to compute the homology classes of cycles on moduli spaces of curves that are defined in terms of Weierstrass points.

This is a preview of subscription content, access via your institution.

References

  1. 1

    Arbarello E., de Concini C., Kac V.G., Procesi C.: Moduli spaces of curves and representation theory. Commun. Math. Phys. 117(1), 1–36 (1988)

    ADS  MATH  Article  Google Scholar 

  2. 2

    Bini G.: Generalized Hodge classes on the moduli space of curves. Beiträge Algebra Geom. 44(2), 559–565 (2003)

    MathSciNet  MATH  Google Scholar 

  3. 3

    Fulton, W.: Equivariant Cohomology in Algebraic Geometry. Lecture Notes by D. Anderson (2007)

  4. 4

    Griffiths P., Harris J.: Principles of Algebraic Geometry. Wiley, New York (1978)

    MATH  Google Scholar 

  5. 5

    Goresky M., Kottwitz R., MacPherson R.: Equivariant cohomology, Koszul duality, and the localization theorem. Invent. Math. 131(1), 25–83 (1998)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  6. 6

    Kempf G., Laksov D.: The determinantal formula of schubert calculus. Acta Math. 132, 153–162 (1974)

    MathSciNet  MATH  Article  Google Scholar 

  7. 7

    Kawazumi N.: A generalization of the Morita–Mumford classes to extended mapping class groups for surfaces. Invent. Math. 131(1), 137–149 (1998)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  8. 8

    Lam, T., Shimozono, M.: k-double Schur functions and equivariant (co)homology of affine Grassmannian, arXiv: 1105.2170

  9. 9

    Liou, J., Schwarz, A.: Equivariant cohomology of infinite-dimensional Grassmannian and shifted Schur functions. Math. Res. Lett. 19(4), 775–784 (2012). arXiv:1201.2554

    Google Scholar 

  10. 10

    Liou, J., Schwarz, A.: Weierstrass cycles in moduli spaces and the Krichever map, arXiv:1207.0530

  11. 11

    Mumford, D.: Towards an Enumerative Geometry of the Moduli Space of Curves. In: Arithmetic and Geometry, vol. II, pp. 271–328. Progr. Math., vol. 36. Birkhäuser, Boston (1983)

  12. 12

    Mulase, M.,: Algebraic theory of the KP equations. In: Perspective in Mathematical Physics, pp. 151–217 (1994)

  13. 13

    Macdonald I.G.: Symmetric functions and Hall polynomials. Clarendon Press, Oxford (1995)

    MATH  Google Scholar 

  14. 14

    Okounkov, A., Olshanski, G.,: Shifted Schur Functions, St. Petersburg Math. J. 9, 239–300 (1998)

    Google Scholar 

  15. 15

    Okounkov, A., Olshanski, G.,: Shifted Schur Functions II. In: The Binomial Formula for Characters of Classical Groups and its Applications. Kirillov’s Seminar on Representation Theory, pp. 245–271. Amer. Math. Soc. Transl. Ser. 2, 181. Amer. Math. Soc., Providence (1998)

  16. 16

    Pressley A., Segal G.: Loop groups. Oxford Mathematical Monographs. Oxford Science Publications, New York (1986)

    Google Scholar 

  17. 17

    Segal, G., Wilson, G.: Loop groups and equations of KdV type. Inst. Hautes Etudes Sci. Publ Math. no. 61, 5–65 (1985)

    Google Scholar 

  18. 18

    Sen A., Zwiebach B.: Quantum background independence of closed string field theory. Nucl. Phys. B 423(2–3), 580–630 (1994)

    MathSciNet  ADS  Article  Google Scholar 

  19. 19

    Schwarz A.: Grassmannian and String theory. Commun. Math. Phys. 199(1), 1–24 (1998)

    ADS  MATH  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. Schwarz.

Additional information

The work was partially supported by NSF grant DMS-0805989.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Liou, JM.(., Schwarz, A. Moduli Spaces and Grassmannian. Lett Math Phys 103, 585–603 (2013). https://doi.org/10.1007/s11005-013-0623-8

Download citation

Mathematics Subject Classification (2010)

  • 14H10
  • 14M15
  • 3E130

Keywords

  • Grassmannian
  • Krichever maps
  • lambda classes
  • moduli spaces
  • Schubert classes