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Torelli theorem for the Deligne--Hitchin moduli space
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abstract
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 $X$.
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Non-Abelian Hodge Theory and Related Topics
A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.
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