Torelli theorem for the Deligne--Hitchin moduli space, II

Abstract

Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d^{\prime }}(X^{\prime },G^{\prime })$ of the associated Deligne--Hitchin moduli spaces are biholomorphic, then X' is isomorphic to X or to the conjugate Riemann surface $\bar{X}$.

10 pages