Nagoya Mathematical Journal

Normality of orbit closures in the enhanced nilpotent cone

Pramod N. Achar, Anthony Henderson, and Benjamin F. Jones

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We continue the study of the closures of GL(V)-orbits in the enhanced nilpotent cone V×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

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

First available in Project Euclid: 18 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B08: Coadjoint orbits; nilpotent varieties
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]


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.

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