Let be a connected reductive affine algebraic group defined over and its Lie algebra. We consider all pairs of the form , where is a complex structure on a compact oriented surface , and is a holomorphic connection on the trivial holomorphic principal -bundle on ; these are known as -differential systems. We study the monodromy map from the space of -differential systems to the character variety of -representations of the fundamental group of . If the complex dimension of is at least three, and , we show that the monodromy map is an immersion at the generic point.
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Indranil Biswas, Sorin Dumitrescu, The Monodromy Map from Differential Systems to the Character Variety Is Generically Immersive. Publ. Res. Inst. Math. Sci. 59 (2023), no. 4, pp. 821–842DOI 10.4171/PRIMS/59-4-5