Point Configurations and Translations

Abstract

The spaces of point configurations on the projective line up to the action of $\mathrm{SL}(2,\mathbb{K})$ and its maximal torus are canonically compactified by the Grothdieck-Knudsen and Losev-Manin moduli spaces ${\overline{M}}_{0,n}$ and ${\overline{L}}_n$ respectively. We examine the configuration space up to the action of the maximal unipotent group ${\mathbb{G}}_a\subseteq \mathrm{SL}(2,\mathbb{K})$ and define an analogous compactification. For this we first assign a canonical quotient to the action of a unipotent group on a projective variety. Moreover, we show that similar to ${\overline{M}}_{0,n}$ and ${\overline{L}}_n$ this quotient arises in a sequence of blow-ups from a product of projective spaces.

26 pages, minor changes

References in corpus (1)

• On the Cox ring of blowing up the diagonal