Explicit upper bound for the Weil-Petersson volumes
Algebraic Geometry
2007-05-23 v2
Abstract
An explicit upper bound for the Weil-Petersson volumes of the moduli spaces of punctured Riemann surfaces is obtained, using Penner's combinatorial integration scheme with embedded trivalent graphs. It is shown that for a fixed number of punctures n and for genus g going to infinity, the Weil-Petersson volume of M_{g,n} has an upper bound c^g g^{2g}. Here c is an independent of n constant, which is given explicitly.
Cite
@article{arxiv.math/0003217,
title = {Explicit upper bound for the Weil-Petersson volumes},
author = {Samuel Grushevsky},
journal= {arXiv preprint arXiv:math/0003217},
year = {2007}
}
Comments
13 pages, AMSTeX. Version 2: misprints and references corrected.