# Algebraic and Geometric Isomonodromic Deformations

@article{Doran2001AlgebraicAG, title={Algebraic and Geometric Isomonodromic Deformations}, author={Charles F. Doran}, journal={Journal of Differential Geometry}, year={2001}, volume={59}, pages={33-85} }

Using the Gauss-Manin connection (Picard-Fuchs differential equation) and a result of Malgrange, a special class of algebraic solutions to isomonodromic deformation equations, the geometric isomonodromic deformations ,i s defined from “families of families” of algebraic varieties. Geometric isomonodromic deformations arise naturally from combinatorial strata in the moduli spaces of elliptic surfaces over P1. The complete list of geometric �

## 37 Citations

Algebraic isomonodromic deformations of logarithmic connections on the Riemann sphere and finite braid group orbits on character varieties

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We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $$n\ge 4$$n≥4 poles, for arbitrary rank. We introduce a natural property of algebraizability…

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We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers…

Heun equations coming from geometry 1

- 2012

We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers…

Painlevé VI Equations with Algebraic Solutions and Family of Curves

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We prove that algebraic solutions of Garnier systems in the irregular case are of two types. The classical ones come from isomonodromic deformations of linear equations with diagonal or dihedral…

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- Computer Science
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The rationality of parameters, trigonometric Diophantine conditions, and what the author calls the Tetrahedral Theorem regarding the absence of algebraic solutions in certain situations are announced.

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We announce some results which might bring a new insight into the classification of algebraic solutions to the sixth Painlevé equation. They consist of the rationality of parameters, trigonometric…

Families of Painlevé VI equations having a common solution

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We classify all functions satisfying non-trivial families of PVI� equations. It turns out that, up to an Okamoto equivalence, there are exactly four families parameterized by affine planes or lines.…

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In this paper we give an overview of the solutions of Fuchsian and non-Fuchsian Riemann-Hilbert problems associated with Frobenius manifold structures on Hurwitz spaces found in recent works of the…

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