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

Pierpaolo Calligaris; Marta Mazzocco

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

Classical Analysis and ODEs 2017-09-11 v2 Mathematical Physics math.MP Exactly Solvable and Integrable Systems

Authors: Pierpaolo Calligaris , Marta Mazzocco

Abstract

In this paper we show that the $SL_{2}(\mathbb C)$ character variety of the Riemann sphere $\Sigma_5$ with five boundary components is a $5$ -parameter family of affine varieties of dimension $4$ . We endow this family of affine varieties with an action of the braid group and classify exceptional finite orbits. This action represents the nonlinear monodromy of the $2$ variable Garnier system and finite orbits correspond to algebraic solutions.

Keywords

pure braid group monodromy Garnier system character variety affine variety finite orbits algebraic solutions

Cite

@article{arxiv.1705.03295,
  title  = {Finite orbits of the pure braid group on the monodromy of the $2$-variable Garnier system},
  author = {Pierpaolo Calligaris and Marta Mazzocco},
  journal= {arXiv preprint arXiv:1705.03295},
  year   = {2017}
}

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39 pages, 1 figure and 3 tables

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

Abstract

Keywords

Cite

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