Explicit upper bound for the Weil-Petersson volumes

Details Explicit upper bound for the Weil-Petersson volumes Explicit upper bound for the Weil-Petersson volumes

2000-03-30

arxiv.org/abs/math/0003217v2

Mathematics

Algebraic Geometry

13 pages, AMSTeX. Version 2: misprints and references corrected.

Scientific paper

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.

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