When is ${\overline{M}}_{0,n}({\mathbb{P}}^1,1)$ a Mori dream space?

Abstract

We prove that the moduli space of $n$-pointed stable maps ${\overline{M}}_{0,n}({\mathbb{P}}^1,1)$ is a Mori dream space whenever the moduli space ${\overline{M}}_{0,n+3}$ of $(n+3)$-pointed rational curves is. We also show that ${\overline{M}}_{0,n}({\mathbb{P}}^1,1)$ is a log Fano variety for $n\le 5$.

Accepted for publication in Advances in Geometry

References in corpus (1)

• On the biregular geometry of the Fulton-MacPherson compactification