ON BIRATIONAL GEOMETRY OF THE SPACE OF PARAMETRIZED RATIONAL CURVES IN GRASSMANNIANS

摘要

In this paper, we study the birational geometry of the Quot schemes of trivial bundles on P-1 by constructing small 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.