A nilpotent orbit of a complex semisimple Lie algebra admits a natural symplectic form. The normalization of its closure is a symplectic variety. Its crepant resolution or Q-factorial terminalization has been extensively studied.
In this lecture, we take a symplectic variety associated with the universal covering of a nilpotent orbit and consider similar problems. When the Lie algebra is classical, we give an explicit algorithm for constructing a Q-factorial terminalization of such a symplectic variety. Moreover, we can give an explicit formula how many different Q-factorial terminalizations it has.
(This is a talk of Tokyo-Kyoto AG seminar on Zoom, and will be given in Japanese.)