Details
| Original language | English |
|---|---|
| Article number | 072 |
| Number of pages | 19 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications |
| Volume | 13 |
| Publication status | Published - 6 Sept 2017 |
Abstract
Let X be a compact connected Riemann surface of genus g ≥ 2, and let M DHbe the rank one Deligne-Hitchin moduli space associated to X. It is known that M DHis the twistor space for the hyper-Kähler structure on the moduli space of rank one holomorphic connections on X. We investigate the group Aut(M DH) of all holomorphic automorphisms of M DH. The connected component of Aut (MDH) containing the identity automorphism is computed. There is a natural element of H 2(M DH;ℤ). We also compute the subgroup of Aut(M DH) that fixes this second cohomology class. Since M DHadmits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that MDH is Moishezon.
Keywords
- math.AG, 14D20, 14J50, 14H60, Hodge moduli space, Deligne-Hitchin moduli space, Moishezon twistor space, λ-connections
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Mathematical Physics
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In: Symmetry, Integrability and Geometry: Methods and Applications, Vol. 13, 072, 06.09.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space
AU - Biswas, Indranil
AU - Heller, Sebastian
N1 - Funding Information: 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.
PY - 2017/9/6
Y1 - 2017/9/6
N2 - Let X be a compact connected Riemann surface of genus g ≥ 2, and let M DHbe the rank one Deligne-Hitchin moduli space associated to X. It is known that M DHis the twistor space for the hyper-Kähler structure on the moduli space of rank one holomorphic connections on X. We investigate the group Aut(M DH) of all holomorphic automorphisms of M DH. The connected component of Aut (MDH) containing the identity automorphism is computed. There is a natural element of H 2(M DH;ℤ). We also compute the subgroup of Aut(M DH) that fixes this second cohomology class. Since M DHadmits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that MDH is Moishezon.
AB - Let X be a compact connected Riemann surface of genus g ≥ 2, and let M DHbe the rank one Deligne-Hitchin moduli space associated to X. It is known that M DHis the twistor space for the hyper-Kähler structure on the moduli space of rank one holomorphic connections on X. We investigate the group Aut(M DH) of all holomorphic automorphisms of M DH. The connected component of Aut (MDH) containing the identity automorphism is computed. There is a natural element of H 2(M DH;ℤ). We also compute the subgroup of Aut(M DH) that fixes this second cohomology class. Since M DHadmits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that MDH is Moishezon.
KW - math.AG
KW - 14D20, 14J50, 14H60
KW - Hodge moduli space
KW - Deligne-Hitchin moduli space
KW - Moishezon twistor space
KW - λ-connections
UR - http://www.scopus.com/inward/record.url?scp=85029181438&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1704.04924
DO - 10.48550/arXiv.1704.04924
M3 - Article
VL - 13
JO - Symmetry, Integrability and Geometry: Methods and Applications
JF - Symmetry, Integrability and Geometry: Methods and Applications
SN - 1815-0659
M1 - 072
ER -