Abstract
Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let \({\mathcal{M}_{{\rm DH}}(X)}\) denote the corresponding \({\text{SL}(r, {\mathbb{C}})}\) Deligne–Hitchin moduli space. We prove that the complex analytic space \({\mathcal{M}_{{\rm DH}}(X)}\) 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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Communicated by N. A. Nekrasov
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Biswas, I., Gómez, T.L., Hoffmann, N. et al. Torelli Theorem for the Deligne–Hitchin Moduli Space. Commun. Math. Phys. 290, 357–369 (2009). https://doi.org/10.1007/s00220-009-0831-3
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DOI: https://doi.org/10.1007/s00220-009-0831-3