Skip to main content
SpringerLink
Log in

The Virtual Class of the Moduli Stack of Stable r-Spin Curves

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We recall the outline of the Seely-Singer-Witten construction of the virtual class on the moduli of stable r-spin curves. We prove that the obtained classes satisfy the axioms of Jarvis-Kimura-Vaintrob.

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

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.

References

  1. Chen, W.: A Homotopy theory of orbispaces, http://arxiv.org/list/math.AT/0102020, 2001

  2. Fujita, H., Kuroda, S.T.: Functional Analysis I (in Japanese). Tokyo: Iwanami Shoten, 1983

  3. Jarvis, T.: Geometry of the moduli of higher spin curves. Internat. J. Math. 11, 637–663 (2000)

    MATH  MathSciNet  Google Scholar 

  4. Jarvis, T.: Torsion-free sheaves and moduli of generalized spin curves. Composito Math. 110: 291–333 (1998)

    Google Scholar 

  5. Jarvis, T.: The Picard group of the moduli of higher spin curves. New York J. Math. 7, 23–47 (2001)

    MATH  MathSciNet  Google Scholar 

  6. Jarvis, T., Kimura, T., Vaintrob, A.: Moduli spaces of higher spin curves and integrable hierarchies. Composito Math. 126, 157–212 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Jarvis, T., Kimura, T., Vaintrob, A.: Gravitational descendents and the moduli space of higher spin curves. In: Advances in algebraic geometry motivated by physics (Lowell, MA, 2000). Contemp. Math. 276, pp. 167–177, 2001

  8. Jarvis, T., Kimura, T., Vaintrob, A.: Spin Gromov-Witten Invariants. Commun. Math. Phys. 259, no. 3, 511–543 (2005)

    Google Scholar 

  9. Polishchuk, A.: Witten's top Chern class on the moduli space of higher spin curves. In : Frobenius manifolds, Aspects Math. Wiesbaden: Vieweg, E36, pp. 253–264, 2004

  10. Polishchuk, A., Vaintrob, A.: Algebraic construction of Witten's top Chern class. In: Advances in algebraic geometry motivated by physics (Lowell, MA, 2000). Contemp. Math. 276, pp. 229–249, 2001

  11. Seely, R., Singer, I.M.: Extending to Singular Riemann Surfaces. J. Geom. Phys. 5, 121–136 (1989)

    Article  Google Scholar 

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

    Google Scholar 

  13. Witten, E.: Algebraic geometry associated with matrix models of two dimensional gravity. In: Topological methods in modern mathematics (Stony Brook, NY, 1991), Houston, TX: Publish or Perish, pp. 235–269, 1993

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Takuro Mochizuki

  2. Max-Planck Institute for Mathematics, Vivatsgasse 7, 53111, Bonn, Germany

    Takuro Mochizuki

Authors
  1. Takuro Mochizuki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Takuro Mochizuki.

Additional information

Communicated by N.A. Nekrasov

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mochizuki, T. The Virtual Class of the Moduli Stack of Stable r-Spin Curves. Commun. Math. Phys. 264, 1–40 (2006). https://doi.org/10.1007/s00220-006-1538-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-006-1538-3

Keywords

Search

Navigation