On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves

Details On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves On the Homology of Certain Smooth Covers of Moduli Spaces of Algebraic Curves

2010-06-22

arxiv.org/abs/1006.4322v3

Mathematics

Algebraic Geometry

15 pages, 12 figures; proof added, corrections

Scientific paper

We suggest a general method of computation of the homology of certain smooth covers $\hat{\mathcal{M}}_{g,1}(\mathbb{C})$ of moduli spaces $\mathcal{M}_{g,1}\br{\mathbb{C}}$ of pointed curves of genus $g$. Namely, we consider moduli spaces of algebraic curves with level $m$ structures. The method is based on the lifting of the Strebel-Penner stratification $\mathcal{M}_{g,1}\br{\mathbb{C}}$. We apply this method for $g\leq 2$ and obtain Betti numbers; these results are consistent with Penner and Harer-Zagier results on Euler characteristics.

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