Abstract
Let S (respectively, S') be a finite subset of a compact connected Riemann surface X (respectively, X') of genus at least two. Let [script M] (respectively, [script 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 [script M] is isomorphic to [script M]' if and only if there is an isomorphism of X with X' taking S to S'.
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