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

Abstract

The open subvariety ${\overline{M}}_g^{\le k}$ 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 ${\overline{M}}_g^{\le k}$ 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 ${\overline{H}}_g^{\le k}$ (the hyperelliptic locus) which has non-vanishing cohomology in degree $3g-2$.

11 pages, 4 figures. To appear in International Mathematics Research Notes

References in corpus (1)

• Two-dimensional topological gravity and equivariant cohomology