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

Author: Atsushi Ito
Journal: Trans. Amer. Math. Soc. 369 (2017), 6279-6301
MSC (2010): Primary 14C20, 14M99
Published electronically: March 1, 2017
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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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Additional Information

Atsushi Ito
Affiliation: Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

Keywords: Quot scheme, small $\mathbb{Q}$-factorial modification, Mori dream space
Received by editor(s): August 12, 2015
Received by editor(s) in revised form: September 19, 2015
Published electronically: March 1, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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