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We give some concrete examples of moduli spaces of connections. Precisely, weexplain how to explicitly construct the moduli spaces of rank 2 fuchsiansystems and logarithmic connections on the Riemann sphere with 4 poles. Theformer ones are affine cubic surfaces; the latter ones are analyticallyisomorphic to affine surfaces but not algebraically: they do not carry nonconstant regular functions. We end with some remark on arbitrary number ofpoles.

Introduction to moduli spaces of connections: some explicit constructions