On [formula omitted]-factorial terminalizations of nilpotent orbits

Abstract

In a recent preprint, Y. Namikawa proposed a conjecture on Q -factorial terminalizations of nilpotent orbit closures and he proved his conjecture for classical simple Lie algebras. In this paper, we prove his conjecture for exceptional simple Lie algebras. For the birational geometry, contrary to the classical case, two new types of Mukai flops appear. We also give classifications of nilpotent orbit closures in simple Lie algebras whose normalization has only Q -factorial or terminal singularities.