Modular operads of embedded curves

Abstract

For each $k\ge 5$, we construct a modular operad ${\overline{\mathcal{ℰ}}}^k$ of “$k$–log-canonically embedded” curves. We also construct, for $k\ge 2$, a stable cyclic operad ${\overline{\mathcal{ℰ}}}_c^k$ of such curves, and, for $k\ge 1$, a cyclic operad ${\overline{\mathcal{ℰ}}}_{0,c}^k$ of “$k$–log-canonically embedded” rational curves.