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On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space
Інший ID:
2010 Mathematics Subject Classification: 14D20; 14J50; 14H60
DOI:10.3842/SIGMA.2017.072
DOI:10.3842/SIGMA.2017.072
Посилання:
On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space / I. Biswas, S. Heller // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 14 назв. — англ.
Підтримка:
We thank the referees for their detailed and helpful comments. The work begun during a research
stay of the second author at the Tata Institute of Fundamental Research and he would like to
thank the institute for its hospitality. SH is partially supported by DFG HE 6818/1-2. The first
author is partially supported by a J.C. Bose Fellowship.
Дата:
2017
Переглядів:
412
Завантажень:
234
Анотація:
Let X be a compact connected Riemann surface of genus g≥2, and let MDH be the rank one Deligne-Hitchin moduli space associated to X. It is known that MDH is 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 MDH admits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that MDH is Moishezon.
