Jet Schemes of Locally Complete Intersection Canonical Singularities
Algebraic Geometry
2009-10-31 v5
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.
Keywords
Cite
@article{arxiv.math/0008002,
title = {Jet Schemes of Locally Complete Intersection Canonical Singularities},
author = {Mircea Mustata},
journal= {arXiv preprint arXiv:math/0008002},
year = {2009}
}
Comments
With an appendix by David Eisenbud and Edward Frenkel. Final version, to appear in Inventiones Mathematicae