On the automorphisms of a rank one Deligne-Hitchin moduli space

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Biswas, I.; Heller, S.: On the automorphisms of a rank one Deligne-Hitchin moduli space. In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 13 (2017), 72. DOI: https://doi.org/10.3842/SIGMA.2017.072

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To cite the version in the repository, please use this identifier: https://doi.org/10.15488/2037

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Abstract: 
Let X be a compact connected Riemann surface of genus g ≥ 2, and let MDHbe the rank one Deligne-Hitchin moduli space associated to X. It is known that MDHis the twistor space for the hyper-Kähler structure on the moduli space of rank one holomorphic connections on X. We investigate the group Aut(MDH) of all holomorphic automorphisms of MDH. The connected component of Aut (MDH) containing the identity automorphism is computed. There is a natural element of H2(MDH;ℤ). We also compute the subgroup of Aut(MDH) that fixes this second cohomology class. Since MDHadmits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that MDH is Moishezon. © 2017, Institute of Mathematics. All rights reserved.
License of this version: CC BY-SA 4.0 Unported
Document Type: article
Publishing status: publishedVersion
Issue Date: 2017
Appears in Collections:Fakultät für Mathematik und Physik

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1 image of flag of Germany Germany 66 95.65%
2 image of flag of United States United States 2 2.90%
3 image of flag of Canada Canada 1 1.45%

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