On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148776 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862657591898800128 |
|---|---|
| author | Biswas, I. Heller, S. |
| author_facet | Biswas, I. Heller, S. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-02T06:19:31Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148776 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T06:19:31Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Biswas, I. Heller, S. 2019-02-18T18:50:13Z 2019-02-18T18:50:13Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 14D20; 14J50; 14H60 DOI:10.3842/SIGMA.2017.072 https://nasplib.isofts.kiev.ua/handle/123456789/148776 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space Article published earlier |
| spellingShingle | On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space Biswas, I. Heller, S. |
| title | On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space |
| title_full | On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space |
| title_fullStr | On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space |
| title_full_unstemmed | On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space |
| title_short | On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space |
| title_sort | on the automorphisms of a rank one deligne-hitchin moduli space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148776 |
| work_keys_str_mv | AT biswasi ontheautomorphismsofarankonedelignehitchinmodulispace AT hellers ontheautomorphismsofarankonedelignehitchinmodulispace |