Normality of orbit closures in the enhanced nilpotent cone

Abstract

We continue the study of the closures of $GL\left(V\right)$-orbits in the enhanced nilpotent cone $V\times \mathcal{N}$ begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal.