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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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148776 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148776 |
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dspace |
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irk-123456789-1487762019-02-19T01:23:35Z On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space Biswas, I. Heller, S. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148776 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Biswas, I. Heller, S. |
| spellingShingle |
Biswas, I. Heller, S. On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Biswas, I. Heller, S. |
| author_sort |
Biswas, I. |
| title |
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_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_sort |
on the automorphisms of a rank one deligne-hitchin moduli space |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148776 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT biswasi ontheautomorphismsofarankonedelignehitchinmodulispace AT hellers ontheautomorphismsofarankonedelignehitchinmodulispace |
| first_indexed |
2023-05-20T17:31:16Z |
| last_indexed |
2023-05-20T17:31:16Z |
| _version_ |
1796153486050590720 |