Quivers and moduli spaces of pointed curves of genus zero

TL;DR

This paper constructs moduli spaces of quiver representations over arbitrary schemes and interprets classical moduli spaces of genus zero pointed curves as inverse limits of these quiver moduli spaces.

Contribution

It introduces a novel perspective by linking moduli spaces of pointed genus zero curves to inverse limits of quiver representation moduli spaces, extending to Hassett spaces.

Findings

Classical moduli spaces are inverse limits of quiver moduli spaces

Constructs moduli spaces of quiver representations over arbitrary schemes

Extends interpretation to Hassett moduli spaces

Abstract

We construct moduli spaces of representations of quivers over arbitrary schemes and show how moduli spaces of pointed curves of genus zero like the Grothendieck-Knudsen moduli spaces $\overline{M}_{0,n}$ and the Losev-Manin moduli spaces $\overline{L}_n$ can be interpreted as inverse limits of moduli spaces of representations of certain bipartite quivers. We also investigate the case of more general Hassett moduli spaces $\overline{M}_{0,a}$ of weighted pointed stable curves of genus zero.