A Torelli theorem for the moduli space of parabolic rank two vector bundles over curves.

Abstract

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 two over X (respectively, X') with fixed determinant of degree one,having a nontrivial quasi-parabolic structure over each point of S (respectively, S'), and of parabolic degree less than two. It is proved that M is isomorphic to M' if and only if there is an isomorphism of X with X' taking S to S'.