Torelli theorem for the Deligne--Hitchin moduli space
Indranil Biswas, Tomas L. Gomez, Norbert Hoffmann, Marina Logares

TL;DR
This paper proves that the Deligne--Hitchin moduli space associated with a Riemann surface uniquely determines the surface and its conjugate, extending Torelli-type results to this complex geometric setting.
Contribution
It establishes a Torelli theorem for the Deligne--Hitchin moduli space, showing it encodes the surface and its conjugate up to isomorphism.
Findings
The Deligne--Hitchin moduli space determines the Riemann surface and its conjugate.
The result applies for genus g ≥ 3 and rank r ≥ 2 (r ≥ 3 if g=3).
Provides a Torelli-type theorem in complex geometry.
Abstract
Fix integers and , with if . Given a compact connected Riemann surface of genus , let denote the corresponding Deligne--Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on .
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