Birational geometry for the covering of a nilpotent orbit closure

A nilpotent orbit $O$ of a complex semisimple Lie algebra $\mathfrak{ g}$ has finite fundamental group. Associated with an etale cover of $O$, we have a finite cover of the closure $\bar{ O}$ of $O$. In this article we consider the finite cover X associated with the universal cover of a nilpotent orbit $O$ of a classical simple Lie algebra $\mathfrak{ g}$. We construct explicitly a Q-factorial terminalization of X in a group theoretic way.

Categories: math.AG math.RT