Torelli theorem for the moduli space of symplectic parabolic Higgs bundles

Abstract

Let (X,D) and (X′,D′) be two compact Riemann surfaces of genus g≥4 with the set of marked points D⊂X and D′⊂X′. Fix a parabolic line bundle L with trivial parabolic structure. Let NSp(2m,α,L) and NSp′(2m,α,L) be the moduli spaces of stable symplectic parabolic Higgs bundles over X and X′ respectively, with rank 2m and fixed parabolic structure α, with the symplectic form taking values in L. We prove that if NSp(2m,α,L) is isomorphic to NSp′(2m,α,L), then there exist an isomorphism between X and X′ sending D to D′.