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arXiv · 1409.0219

On birational geometry of the space of parametrized rational curves in Grassmannians

Atsushi Ito
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Abstract

In this paper, we study the birational geometry of the Quot schemes of trivial bundles on $\mathbb{P}^1$ by constructing small $\mathbb{Q}$-factorial modifications of the Quot schemes as suitable moduli spaces. We determine all the models which appear in the minimal model program on the Quot schemes. As a corollary, we show that the Quot schemes are Mori dream spaces and log Fano.

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Atsushi Ito. 2014-08-31. On birational geometry of the space of parametrized rational curves in Grassmannians. https://arxiv.org/abs/1409.0219

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