Jet schemes of determinantal varieties
  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 $(\mathbb{A}^{rs},X)$. 
Cornelia Yuen