Geodesic
On the Tau Function for the Schlesinger Equation of Isomonodromic Deformations
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 184-191 
A. A. Bolibrukh. On the Tau Function for the Schlesinger Equation of Isomonodromic Deformations. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 184-191. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a1/
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     title = {On the {Tau} {Function} for the {Schlesinger} {Equation} of {Isomonodromic} {Deformations}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The tau function for the Schlesinger equation of isomonodromic deformations is represented as the result of successively applied elementary gauge transformations; this, in particular, suggests a simple proof for the Miwa theorem about the tau function.

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[3] Bolibruch A. A., “On orders of movable poles of the Schlesinger equation”, J. Dynam. Control Systems, 6:1 (2000), 57–74 | DOI | MR

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[5] Okonek K., Shneider M., Shpindler Kh., Vektornye rassloeniya na kompleksnom proektivnom prostranstve, Mir, M., 1984 | Zbl

[6] Bolibruch A. A., “Vector bundles associated with monodromies and asymptotics of Fuchsian systems”, J. Dynam. Control Systems, 1:1 (1995), 229–252 | DOI | MR | Zbl