WeilPetersson volumes and intersection theory on the moduli space of curves
Abstract
In this paper, we establish a relationship between the Weil Petersson volume V_{g,n}(b) of the moduli space {M}_{g,n}(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b_{1},ldots, b_{n} , and the intersection numbers of tautological classes on the moduli space overline{{M}}_{g,n} of stable curves. As a result, by using the recursive formula for V_{g,n}(b) obtained in the author's Simple geodesics and WeilPetersson volumes of moduli spaces of bordered Riemann surfaces, preprint, 2003, we derive a new proof of the Virasoro constraints for a point. This result is equivalent to the WittenKontsevich formula.
 Publication:

Journal of the American Mathematical Society
 Pub Date:
 January 2007
 DOI:
 10.1090/S0894034706005261
 Bibcode:
 2007JAMS...20....1M