Jet schemes of determinantal varieties

Details Jet schemes of determinantal varieties Jet schemes of determinantal varieties

2006-08-25

arxiv.org/abs/math/0608632v1

Mathematics

Algebraic Geometry

10 pages, this is part of the author's PhD thesis at the University of Michigan

Scientific paper

This article studies the scheme structure of the jet schemes of determinantal varieties. We show that in general, these jet schemes are not irreducible. In the case of the determinantal variety $X$ of $r \times s$ matrices of rank at most one, we give a formula for the dimension of each of the components of its jet schemes. As an application, we compute the log canonical threshold of the pair $(\mathbb{A}^{rs},X)$.

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