Integrable systems and Torelli theorems for the moduli spaces of parabolic bundles and parabolic Higgs bundles (Q2810693)

The classical theorem by Torelli says that a smooth complex algebraic curve is determined by the isomorphism class of its polarized Jacobian up to isomorphism. In this paper, the authors 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 they 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 \textit{J. C. Hurtubise} [Duke Math. J. 83, No. 1, 19--50 (1996; Zbl 0857.58024); erratum ibid. 84, No. 3, 815 (1996)].