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ALGEBRAIC ISOMONODROMIC DEFORMATIONS AND THE MAPPING CLASS GROUP

Abstract : The germ of the universal isomonodromic deformation of a logarithmic connection on a stable n-pointed genus-g curve always exists in the analytic category. The first part of this paper investigates under which conditions it is the analytic germification of an algebraic isomonodromic deformation. Up to some minor technical conditions, this turns out to be the case if and only if the monodromy of the connection has finite orbit under the action of the mapping class group. The second part of this paper studies the dynamics of this action in the particular case of reducible rank 2 representations and genus g > 0, allowing to classify all finite orbits. Both of these results extend recent ones concerning the genus 0 case.
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Submitted on : Thursday, January 12, 2017 - 11:40:43 AM
Last modification on : Friday, April 1, 2022 - 3:57:36 AM
Long-term archiving on: : Friday, April 14, 2017 - 2:22:01 PM

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Gaël Cousin, Viktoria Heu. ALGEBRAIC ISOMONODROMIC DEFORMATIONS AND THE MAPPING CLASS GROUP. Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), 2021, 20 (5), pp.1497-1545. ⟨10.1017/S1474748019000562⟩. ⟨hal-01432947⟩

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