Torelli Theorem for the Deligne--Hitchin Moduli Space, II

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 $\CC$. If some components $\MDH^d(X,G)$ and $\MDH^{d'}(X',G')$ of the associated Deligne--Hitchin moduli spaces are biholomorphic, then $X'$ is isomorphic to $X$ or to the conjugate Riemann surface $\Xbar$.

2010 Mathematics Subject Classification: 14D20, 14C34

Keywords and Phrases: Principal bundle, Deligne--Hitchin moduli space, Higgs bundle, vector field

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