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On the rational cohomology of moduli spaces of curves with level structures

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Abstract

We investigate low degree rational cohomology groups of smooth compactifications of moduli spaces of curves with level structures. In particular, we determine \({H^k\left({\bar S}_{g}, {\mathbb Q}\right)}\) for g ≥ 2 and k ≤ 3, where \({{\bar S}_{g}}\) denotes the moduli space of spin curves of genus g.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133, Milan, Italy

    Gilberto Bini

  2. Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, 38123, Trento, Italy

    Claudio Fontanari

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  1. Gilberto Bini
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  2. Claudio Fontanari
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Correspondence to Gilberto Bini.

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Bini, G., Fontanari, C. On the rational cohomology of moduli spaces of curves with level structures. Geom Dedicata 156, 127–139 (2012). https://doi.org/10.1007/s10711-011-9593-0

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  • DOI: https://doi.org/10.1007/s10711-011-9593-0

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