Jet Schemes of Locally Complete Intersection Canonical Singularities

Details Jet Schemes of Locally Complete Intersection Canonical Singularities Jet Schemes of Locally Complete Intersection Canonical Singularities

2000-08-01

arxiv.org/abs/math/0008002v5

Invent. Math. 145 (2001), no. 3, 397--424.

Mathematics

Algebraic Geometry

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

Scientific paper

10.1007/s002220100152

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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