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Jet Schemes of Locally Complete Intersection Canonical Singularities

Mircea Mustata
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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.

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Mircea Mustata. 2001-04-09. Jet Schemes of Locally Complete Intersection Canonical Singularities. https://doi.org/10.1007/s002220100152

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