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arXiv · 2001.05554

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

Claudio Fontanari
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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 $n \le 5$.

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Claudio Fontanari. 2020-01-15. When is $\overline{M}_{0,n}(\mathbb{P}^1,1)$ a Mori dream space?. https://arxiv.org/abs/2001.05554

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