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arXiv · 2002.05927

The monodromy map from differential systems to character variety is generically immersive

Indranil Biswas·Sorin Dumitrescu
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Abstract

Let $G$ be a connected reductive affine algebraic group defined over $\mathbb C$ and $\mathfrak g$ its Lie algebra. We study the monodromy map from the space of $\mathfrak g$-differential systems on a compact connected Riemann surface $\Sigma$ of genus $g \,\geq\, 2$ to the character variety of $G$-representations of the fundamental group of $\Sigma$. If the complex dimension of $G$ is at least three, we show that the monodromy map is an immersion at the generic point.

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Indranil Biswas, Sorin Dumitrescu. 2020-02-14. The monodromy map from differential systems to character variety is generically immersive. https://arxiv.org/abs/2002.05927

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