The dependence on the monodromy data of the isomonodromic tau function

Understand

[Note: important Corrigendum now available at arXiv:1601.04790] The isomonodromic tau function defined by Jimbo-Miwa-Ueno vanishes on the Malgrange's divisor of generalized monodromy data for which a vector bundle is nontrivial, or, which is the same, a certain Riemann-Hilbert problem has no solution.

• In their original work, Jimbo, Miwa, Ueno did not derive the dependence on the (generalized) monodromy data (i.e.
• monodromy representation and Stokes' parameters).
• We fill the gap by providing a (simpler and more general) description in which all the parameters of the problem (monodromy-changing and monodromy-preserving) are dealt with at the same level.