Moduli space of logarithmic connections singular over a finite subset of a compact Riemann surface

Let $S$ be a finite subset of compact connected Riemann surface $X$ genus $g \geq 2$. $\cat{M}_{lc}(n,d)$ denote the moduli space pairs $(E,D)$, where $E$ is holomorphic vector bundle over and $D$ logarithmic connection on singular $S$, with fixed residues in centre $\mathfrak{gl}(n,\C)$, $n$ $d$ are mutually corpime. $L$ line $D_L$ $S$. $\cat{M}'_{lc}(n,d)$ $\cat{M}_{lc}(n,L)$ spaces parametrising all $(E,D)$ such that underlying stable $(\bigwedge^nE, \tilde{D}) \cong (L,D_L)$ respectively. Let $\cat{M}'_{lc}(n,L) \subset \cat{M}_{lc}(n,L)$ Zariski open dense stable. We show there natural compactification $\cat{M}'_{lc}(n,L)$ compute their Picard groups. We also hence do not have any non-constant algebraic functions but they admit holomorhic functions. study group connections arbitrary residues.