Skip to main content
SpringerLink
Log in

On the cohomology of the Losev–Manin moduli space

  • Published:
Manuscripta Mathematica Aims and scope Submit manuscript

Abstract

We determine the cohomology of the Losev–Manin moduli space \({\overline{M}_{0, 2 | n}}\) of pointed genus zero curves as a representation of the product of symmetric groups \({\mathbb{S}_2 \times \mathbb{S}_n}\).

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. Batyrev V., Blume M.: The functor of toric varieties associated with Weyl chambers and Losev–Manin moduli spaces. Tohoku Math. J. (2) 63(4), 581–604 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dolgachev I., Lunts V.: A character formula for the representation of a Weyl group in the cohomology of the associated toric variety. J. Algebra 168(3), 741–772 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hassett B.: Moduli spaces of weighted pointed stable curves. Adv. Math. 173(2), 316–352 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kapranov M.M.: Chow quotients of Grassmannians. I. Adv. Sov. Math. 16, 29–110 (1993)

    MathSciNet  Google Scholar 

  5. Lehrer G.I.: Rational points and Coxeter group actions on the cohomology of toric varieties. Ann. Inst. Fourier (Grenoble) 58(2), 671–688 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Losev A., Manin Y.: New moduli spaces of pointed curves and pencils of flat connections. Mich. Math. J. 48, 443–472 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2 ed, p. x+475. The Clarendon Press, Oxford University Press, New York (1995)

  8. Marian A., Oprea D., Pandharipande R.: The moduli space of stable quotients. Geom. Topol. 15, 1651–1706 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Procesi, C.: The toric variety associated to Weyl chambers. In: Mots, Lang. Raison. Calc., Hermés, Paris, pp. 153–161 (1990)

  10. Shadrin S., Zvonkine D.: A group action on Losev–Manin cohomological field theories. Ann. Inst. Fourier (Grenoble) 61(7), 2719–2743 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  11. Stanley, R.P.: Log-concave and unimodal sequences in algebra, combinatorics, and geometry. In: Graph theory and its applications: East and West (Jinan, 1986), vol. 576, pp. 500–535. New York Acad. Sci. New York (1989)

  12. Stembridge J.R.: Some permutation representations of Weyl groups associated with the cohomology of toric varieties. Adv. Math. 106(2), 244–301 (1994)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Matematiska institutionen, Stockholms Universitet, 106 91, Stockholm, Sweden

    Jonas Bergström

  2. Department of Mathematics, Tokyo Denki University, Tokyo, 120-8551, Japan

    Satoshi Minabe

Authors
  1. Jonas Bergström
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Satoshi Minabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonas Bergström.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bergström, J., Minabe, S. On the cohomology of the Losev–Manin moduli space. manuscripta math. 144, 241–252 (2014). https://doi.org/10.1007/s00229-013-0647-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-013-0647-5

Mathematics Subject Classification (2000)

Search

Navigation