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

Claudio Fontanari

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

Algebraic Geometry 2020-01-17 v1

Authors: Claudio Fontanari

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 $n \le 5$ .

Cite

@article{arxiv.2001.05554,
  title  = {When is $\overline{M}_{0,n}(\mathbb{P}^1,1)$ a Mori dream space?},
  author = {Claudio Fontanari},
  journal= {arXiv preprint arXiv:2001.05554},
  year   = {2020}
}

Comments

Accepted for publication in Advances in Geometry

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