## Nagoya Mathematical Journal

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

#### Abstract

We continue the study of the closures of $\operatorname{GL}(V)$-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.

#### Article information

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

Dates
First available in Project Euclid: 18 August 2011

https://projecteuclid.org/euclid.nmj/1313682311

Digital Object Identifier
doi:10.1215/00277630-1331854

Mathematical Reviews number (MathSciNet)
MR2834248

Zentralblatt MATH identifier
1252.17005

#### Citation

Achar, Pramod N.; Henderson, Anthony; Jones, Benjamin F. Normality of orbit closures in the enhanced nilpotent cone. Nagoya Math. J. 203 (2011), 1--45. doi:10.1215/00277630-1331854. https://projecteuclid.org/euclid.nmj/1313682311

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