Abstract
In this chapter we illustrate some of the consequences of the orbicellular decomposition of \(\overline{M}_{g, P}\) described in the previous chapter. More specifically, we begin by showing that the rational homology of moduli of smooth curves vanishes in sufficiently high degree. From this, we compute the low degree cohomology of moduli of smooth and stable curves. Based on the cellular decomposition, and following Kontsevich, we then give combinatorial expressions for the classes of the point bundles and for a volume form on moduli, which are both of central importance in the next chapter.
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© 2011 Springer-Verlag Berlin Heidelberg
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Arbarello, E., Cornalba, M., Griffiths, P.A. (2011). First consequences of the cellular decomposition. In: Geometry of Algebraic Curves. Grundlehren der mathematischen Wissenschaften, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69392-5_11
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DOI: https://doi.org/10.1007/978-3-540-69392-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42688-2
Online ISBN: 978-3-540-69392-5
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