Integrable systems and Torelli theorems for the moduli spaces of   parabolic bundles and parabolic Higgs bundles
  We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using this result we also prove a Torelli theorem for the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights. The key input in the proofs is a method of J.C. Hurtubise, Integrable systems and algebraic surfaces, Duke Math. Jour. 83 (1996), 19--49. 
Indranil Biswas, Tom\'as L. G\'omez, Marina Logares
math.AG