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On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space

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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Main Authors: Biswas, I., Heller, S.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148776
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spelling 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
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