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

Atsushi Ito

Published 2014-08-31Version 1

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