Finite orbits of the pure braid group on the monodromy of the $2$-variable Garnier system

Calligaris, Pierpaolo; Mazzocco, Marta

doi:10.48550/arxiv.1705.03295

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Algebraic Solutions Of Irregular Garnier Systems: Examples A...1

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2020

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“…This is not using this trichotomy that algebraic solutions of Painlevé VI equation were found, but by brute force, which seems out of reach even in the case N = 2. Recently, Calligaris and Mazzocco [9] gave a partial classification by using confuence of poles in order to exploit the Painlevé classification [35].…”

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confidence: 99%

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Classification of algebraic solutions of irregular Garnier systems

Diarra¹,

Loray²

2020

Compositio Math.

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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 differential Galois group; we give a complete list in the rank N = 2 case (two indeterminates).The pull-back ones come from deformations of coverings over a fixed degenerate hypergeometric equation; we provide a complete list when the differential Galois group is SL 2 (C). By the way, we have a complete list of algebraic solutions for the rank N = 2 irregular Garnier systems.

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Section: Himentioning

confidence: 99%

“…There are several methods to construct algebraic solutions of classical Garnier systems (logarithmic case), see [1,7,9,14,15,16,35] and references therein. In the irregular case, let us describe two methods to produce algebraic isomonodromic deformations.…”

Section: Algebraic Solutions Of Irregular Garnier Systems: Examples A...mentioning

confidence: 99%

Classification of algebraic solutions of irregular Garnier systems

Diarra¹,

Loray²

2020

Compositio Math.

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Finite orbits of the pure braid group on the monodromy of the $2$-variable Garnier system

Cited by 1 publication

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Classification of algebraic solutions of irregular Garnier systems

Classification of algebraic solutions of irregular Garnier systems

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