Two-dimensional cycle classes on $\overline{{\mathcal{M}}_{0,n}}$

Abstract

For each $n\ge 5$, we give an $S_n$-equivariant basis for $H_4(\overline{{\mathcal{M}}_{0,n}},\mathbb{Q})$, as well as for $H_{2(n-5)}(\overline{{\mathcal{M}}_{0,n}},\mathbb{Q})$. Such a basis exists for $H_2(\overline{{\mathcal{M}}_{0,n}},\mathbb{Q})$ and for $H_{2(n-4)}(\overline{{\mathcal{M}}_{0,n}},\mathbb{Q})$, but it is not known whether one exists for $H_{2k}(\overline{{\mathcal{M}}_{0,n}},\mathbb{Q})$ when $3\le k\le n-6$.

11 pages, comments welcome