Isomonodromic deformations of connections with singularities of parahoric formal type

Details Isomonodromic deformations of connections with singularities of parahoric formal type Isomonodromic deformations of connections with singularities of parahoric formal type

2010-10-12

arxiv.org/abs/1010.2292v2

Mathematics

Algebraic Geometry

32 pages. One of the main theorems (Theorem 5.1) has been significantly strengthened. It now states that the isomonodromy equa

Scientific paper

In previous work, the authors have developed a geometric theory of fundamental strata to study connections on the projective line with irregular singularities of parahoric formal type. In this paper, the moduli space of connections that contain regular fundamental strata with fixed combinatorics at each singular point is constructed as a smooth Poisson reduction. The authors then explicitly compute the isomonodromy equations as an integrable system. This result generalizes work of Jimbo, Miwa, and Ueno to connections whose singularities have parahoric formal type.

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