Vol. 281, No. 1, 2016

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Jet schemes of the closure of nilpotent orbits

Anne Moreau and Rupert Wei Tze Yu

Vol. 281 (2016), No. 1, 137–183

We study in this paper the jet schemes of the closure of nilpotent orbits in a finite-dimensional complex reductive Lie algebra. For the nilpotent cone, which is the closure of the regular nilpotent orbit, all the jet schemes are irreducible. This was first observed by Eisenbud and Frenkel, and follows from a strong result of Mustaţă (2001). Using induction and restriction of “little” nilpotent orbits in reductive Lie algebras, we show that for a large number of nilpotent orbits, the jet schemes of their closures are reducible. As a consequence, we obtain certain geometric properties of these nilpotent orbit closures.

nilpotent orbits, jet schemes, induction
Mathematical Subject Classification 2010
Primary: 14L30, 17B20, 17B08
Received: 21 April 2015
Revised: 3 August 2015
Accepted: 3 August 2015
Published: 9 February 2016
Anne Moreau
Laboratoire de Mathématiques et Applications
Universite de Poitiers
Teéléport 2 - BP 30179
Boulevard Marie et Pierre Curie
86962 Futuroscope (Poitiers) Chasseneuil Cedex
Rupert Wei Tze Yu
Laboratoire de Mathématiques de Reims (LMR) - EA 4535
Université de Reims Champagne Ardenne
U.F.R. Sciences Exactes et Naturelles
Moulin de la Housse - BP 1039
51687 Reims Cedex 2