Derivative of the Riemann-Hilbert map

Vladimir Marković; Ognjen Tošić

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arXiv · 2407.03296

Derivative of the Riemann-Hilbert map

Vladimir Marković·Ognjen Tošić

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Abstract

Given a pair $(X,\nabla)$, consisting of a closed Riemann surface $X$ and a holomorphic connection $\nabla$ on the trivial principal bundle $X\times\mathrm{SL}_2(\mathbb{C})\to X$, the Riemann-Hilbert map sends $(X,\nabla)$ to its monodromy representation. We compute the derivative of this map, and provide a simple description of the locus where it is injective, recovering in the process several previously obtained results.

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Vladimir Marković, Ognjen Tošić. 2024-07-03. Derivative of the Riemann-Hilbert map. https://arxiv.org/abs/2407.03296

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