  We introduce a family of local deformations for meromorphic connections on
the Riemann sphere in the neighborhood of a higher rank (simple) singularity.
Following a scheme introduced by Malgrange we use these local models to prove
that the zeros of the tau function introduced by Jimbo, Miwa and Ueno occur
precisely at those points in the deformation space at which a certain
Birkhoff-Riemann- Hilbert problem fails to have a solution.

Exactly Solvable and Integrable Systems;Exactly Solvable and Integrable Systems