Jet Schemes of Locally Complete Intersection Canonical Singularities

Abstract

We prove that if X is a locally complete intersection variety, then X has all the jet schemes irreducible if and only if X has canonical singularities. After embedding X in a smooth variety Y, we use motivic integration to express the condition that X has irreducible jet schemes in terms of data coming from an embedded resolution of X in Y. We show that this condition is equivalent with having canonical singularities. In the appendix, this result is used to prove a generalization of Kostant's freeness theorem to the setting of jet schemes.

With an appendix by David Eisenbud and Edward Frenkel. Final version, to appear in Inventiones Mathematicae

References in corpus (2)

• An introduction to motivic integration
• Rational singularities

Cited by in corpus (62)

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• Positivity of divisors on blown-up projective spaces, II
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• Beilinson-Drinfeld Schubert varieties and global Demazure modules
• Associated varieties and Higgs branches (a survey)
• Lifting mappings over invariants of finite groups
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• Nash multiplicities and resolution invariants
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• On the restricted Verma modules at the critical level
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• Motivic Integration on Toric Stacks
• On jet schemes of pfaffian ideals
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• On reduced arc spaces of toric varieties
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• On the embedded Nash problem
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