Weil-Petersson volumes and intersection theory on the moduli space of curves

Mar 8, 2006
24 pages
Published in:
  • J.Am.Math.Soc. 20 (2007) 01, 1-24
  • Published: Mar 8, 2006

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Abstract:
In this paper, we establish a relationship between the Weil-Petersson volume Vg,n(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b1,...,bn, and the intersection numbers of tautological classes on the moduli space Mg,n of stable curves. As a result, by using the recursive formula for Vg,n(b) obtained in [22], we derive a new proof of the Virasoro constraints for a point. This result is equivalent to the Witten-Kontsevich formula.
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