Birational description of moduli spaces of rank 2 logarithmic connections

In this paper, we provide an explicit description of the Zariski-open subset of the moduli space of rank 2 parabolic logarithmic connections in the case g≥2. Our approach is to analyze the underlying parabolic bundles and the apparent singularities of the parabolic connections. We prove that a Zariski-open subset of the product of a projective space and the moduli space of parabolic bundles give a Darboux coordinate for the moduli space of parabolic connections.