%0 Journal Article
%T Torelli theorem for the Deligne--Hitchin moduli space
%A Indranil Biswas
%A Tomas L. Gomez
%A Norbert Hoffmann
%A Marina Logares
%J Mathematics
%D 2008
%I arXiv
%R 10.1007/s00220-009-0831-3
%X Fix integers $g\geq 3$ and $r\geq 2$, with $r\geq 3$ if $g=3$. Given a compact connected Riemann surface $X$ of genus $g$, let $\MDH(X)$ denote the corresponding $\text{SL}(r, {\mathbb C})$ Deligne--Hitchin moduli space. We prove that the complex analytic space $\MDH(X)$ determines (up to an isomorphism) the unordered pair $\{X, \overline{X}\}$, where $\overline{X}$ is the Riemann surface defined by the opposite almost complex structure on $X$.
%U http://arxiv.org/abs/0901.0021v1