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

@article{Mirzakhani2006WeilPeterssonVA,
title={Weil-Petersson volumes and intersection theory on the moduli space of curves},
author={Maryam Mirzakhani},
journal={Journal of the American Mathematical Society},
year={2006},
volume={20},
pages={1-23}
}
• M. Mirzakhani
• Published 8 March 2006
• Mathematics
• Journal of the American Mathematical Society
In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn, and the intersection numbers of tauto logical 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 [14].
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