Small resolutions of moduli spaces of scaled curves

Abstract

We construct small resolutions of the moduli space ${\overline{Q}}_n$ of stable scaled $n$-marked lines of Ziltener and Ma'u--Woodward and of the moduli space ${\overline{P}}_n$ of stable $n$-marked ${\mathbb{G}}_a$-rational trees introduced in earlier work. The resolution of ${\overline{P}}_n$ is the augmented wonderful variety corresponding to the graphic matroid of the complete graph. The resolution of ${\overline{Q}}_n$ is a further blowup, also a wonderful model of an arrangement in ${\mathbb{P}}^{n-1}$.

39 pages, 4 figures