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arXiv · 1302.5405

The Cohomological Excess of Certain Moduli Spaces of Curves of Genus $g$

Chitrabhanu Chaudhuri
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Abstract

The open subvariety $\overline{M}_g^{\leq k}$ of $\overline{M}_g$ parametrizes stable curves of genus $g$ having at most $k$ rational components. By the work of Looijenga, one expects that the cohomological excess of $\overline{M}_g^{\leq k}$ is at most $g-1+k$. In this paper we show that when $k=0$, the conjectured upper bound is sharp by showing that there is a constructible sheaf on $\overline{H}_g^{\leq k}$ (the hyperelliptic locus) which has non-vanishing cohomology in degree $3g-2$.

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Chitrabhanu Chaudhuri. 2013-11-07. The Cohomological Excess of Certain Moduli Spaces of Curves of Genus $g$. https://doi.org/10.1093/imrn%2Frnt229

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