Torelli theorem for the Deligne-Hitchin moduli space (Pre-published version)

Abstract

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let M DH (X) denote the corresponding SL(r,C) Deligne–Hitchin moduli space. We prove that the complex analytic space M DH (X) determines (up to an isomorphism) the unordered pair {X,X − − } , where X − − is the Riemann surface defined by the opposite almost complex structure on X