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The moduli space of regular stable maps

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Abstract

We prove that the moduli space of regular stable maps in a complex manifold admits a natural complex orbifold structure. Our proof is based on Hardy decompositions and Fredholm intersection theory.

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References

  1. Fulton W. and Pandharipande R. (1997). Notes on stable maps and quantum cohomology. In: Algebraic Geometry-Santa uz 1995 ed. Kollar, Lazersfeld, Morrison. Proc. Symp. Pure Math. 62: 45–96

    MathSciNet  Google Scholar 

  2. McDuff D. and Salamon D.A. (2004). J-holomorphic Curves and Symplectic Topology. AMS Colloquium Publications, Providence

    MATH  Google Scholar 

  3. Milnor J. (1965). Topology from the Differential Viewpoint. Princeton University Press, Princeton

    Google Scholar 

  4. Robbin, J.W., Salamon, D.A.: A construction of the Deligne–Mumford orbifold. J. Eur. Math. Soc. 8, 611–699 (2004). Corrigendum, July 2007, to appear in JEMS.

    Google Scholar 

  5. Ruan Y. and Tian G. (1995). A mathematical theory of quantum cohomology. J. Differ. Geom. 42: 259–367

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, University of Wisconsin, Madison, WI, 53706, USA

    Joel W. Robbin & Yongbin Ruan

  2. Department Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    Dietmar A. Salamon

Authors
  1. Joel W. Robbin
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  2. Yongbin Ruan
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  3. Dietmar A. Salamon
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Corresponding author

Correspondence to Dietmar A. Salamon.

Additional information

The authors would like to thank the referee for his/her diligent work. We are grateful for the careful attention to detail in the report.

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Robbin, J.W., Ruan, Y. & Salamon, D.A. The moduli space of regular stable maps. Math. Z. 259, 525–574 (2008). https://doi.org/10.1007/s00209-007-0237-x

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  • DOI: https://doi.org/10.1007/s00209-007-0237-x

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