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Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0

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Noncommutative Differential Geometry and Its Applications to Physics

Part of the book series: Mathematical Physics Studies ((MPST,volume 23))

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Abstract

Let V be a smooth, projective, convex variety. We define tautological ψ and κ classes on the moduli space of stable maps \( {{\bar{\mathcal{M}}}_{{0,n}}}\left( V \right) \) , give a (graphical) presentation for these classes in terms of boundary strata, derive differential equations for the generating functions of the Gromov-Witten invariants of V twisted by these tautological classes, and prove that these intersection numbers are completely determined by the Gromov-Witten invariants of V. This results in families of genus zero cohomological field theory structures on the cohomology ring of V which includes the quantum cohomology as a special case.

Research of the first author was partially supported by NSF grant number DMS-9803553

Research of the second author was partially supported by NSF grant number DMS-9803427

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich-Irchel, Winterthurerstr. 190, CH-8057, Zürich, Switzerland

    Alexandre Kabanov

  2. Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA, 02215, USA

    Takashi Kimura

Authors
  1. Alexandre Kabanov
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  2. Takashi Kimura
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Editors and Affiliations

  1. Keio University, Yokohama, Japan

    Yoshiaki Maeda , Hitoshi Moriyoshi  & Tatsuya Tate ,  & 

  2. Science University of Tokyo, Noda, Japan

    Hideki Omori

  3. CNRS and Université de Bourgogne, Dijon, France

    Daniel Sternheimer

  4. Tohoku University, Sendai, Japan

    Satoshi Watamura

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Kabanov, A., Kimura, T. (2001). Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_5

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  • DOI: https://doi.org/10.1007/978-94-010-0704-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3829-4

  • Online ISBN: 978-94-010-0704-7

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