A Torelli type theorem for the moduli space of parabolic vector bundles over curves

Let S (respectively, S') be a finite subset of a compact connected Riemann surface X (respectively, X') of genus at least two. Let M (respectively M') denote a moduli space of parabolic stable bundles of rank 2 over X (respectively X') with fixed determinant of degree 1, having a nontrivial quasi-parabolic structure over each point of S (respectively, S') and of parabolic degree less than 2. It, is proved that, K is isomorphic to M' if and only if there is an isomorphism of X with X' taking S to S'.