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

Ito, Atsushi

doi:10.1090/tran/6840

On birational geometry of the space of parametrized rational curves in Grassmannians
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Trans. Amer. Math. Soc. 369 (2017), 6279-6301 Request permission

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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