Normality of orbit closures in the enhanced nilpotent cone

Details Normality of orbit closures in the enhanced nilpotent cone Normality of orbit closures in the enhanced nilpotent cone

2010-04-22

arxiv.org/abs/1004.3822v1

Nagoya Math. J. 203 (2011), 1-45

Mathematics

Representation Theory

30 pages

Scientific paper

10.1215/00277630-1331854

We continue the study of the closures of $GL(V)$-orbits in the enhanced nilpotent cone $V\times\cN$ 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.

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