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Jet schemes of the
closure of nilpotent orbits
Anne Moreau and Rupert Wei Tze Yu |
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Vol. 281 (2016), No. 1, 137–183
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Abstract |
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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. |
Keywords
nilpotent orbits, jet schemes, induction
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Mathematical Subject Classification 2010
Primary: 14L30, 17B20, 17B08
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Milestones
Received: 21 April 2015
Revised: 3 August 2015
Accepted: 3 August 2015
Published: 9 February 2016
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Authors |
| Anne Moreau | |
| Laboratoire de Mathématiques et
Applications Universite de Poitiers Teéléport 2 - BP 30179 Boulevard Marie et Pierre Curie 86962 Futuroscope (Poitiers) Chasseneuil Cedex France |
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| 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 France |
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