Torelli theorem for the moduli space of symplectic parabolic Higgs bundles

Let (X, D) and (X', D') be two compact Riemann surfaces of genus g >= 4 with the set of marked points D subset of X and D' subset of X'. Fix a parabolic line bundle L with trivial parabolic structure. Let N-Sp(2m, alpha, L) and N'(Sp)(2m, alpha, L) be the moduli spaces of stable symplectic parabolic Higgs bundles over X and X' respectively, with rank 2m and fixed parabolic structure alpha, with the symplectic form taking values in L. We prove that if N-Sp(2m, alpha, L) is isomorphic to N'(Sp)(2m, alpha, L), then there exist an isomorphism between X and X' sending D to D'. (C) 2021 Elsevier Masson SAS. All rights reserved.