Loading [MathJax]/extensions/tex2jax.js

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

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Indranil Biswas
  • Sebastian Heller

Organisationseinheiten

Externe Organisationen

  • Tata Institute of Fundamental Research (TIFR HYD)

Details

OriginalspracheEnglisch
Aufsatznummer072
Seitenumfang19
FachzeitschriftSymmetry, Integrability and Geometry: Methods and Applications
Jahrgang13
PublikationsstatusVeröffentlicht - 6 Sept. 2017

Abstract

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$, and let ${\mathcal M}_{\rm DH}$ be the rank one Deligne-Hitchin moduli space associated to $X$. It is known that ${\mathcal M}_{\rm DH}$ is the twistor space for the hyper-K\"ahler structure on the moduli space of rank one holomorphic connections on $X$. We investigate the group $\operatorname{Aut}({\mathcal M}_{\rm DH})$ of all holomorphic automorphisms of ${\mathcal M}_{\rm DH}$. The connected component of $\operatorname{Aut}({\mathcal M}_{\rm DH})$ containing the identity automorphism is computed. There is a natural element of $H^2({\mathcal M}_{\rm DH}, {\mathbb Z})$. We also compute the subgroup of $\operatorname{Aut}({\mathcal M}_{\rm DH})$ that fixes this second cohomology class. Since ${\mathcal M}_{\rm DH}$ admits an ample rational curve, the notion of algebraic dimension extends to it by a theorem of Verbitsky. We prove that ${\mathcal M}_{\rm DH}$ is Moishezon.

ASJC Scopus Sachgebiete

Zitieren

On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space. / Biswas, Indranil; Heller, Sebastian.
in: Symmetry, Integrability and Geometry: Methods and Applications, Jahrgang 13, 072, 06.09.2017.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Biswas I, Heller S. On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space. Symmetry, Integrability and Geometry: Methods and Applications. 2017 Sep 6;13:072. doi: 10.48550/arXiv.1704.04924, 10.3842/SIGMA.2017.072
Download
@article{2b680e1197c6461a840447baab299d81,
title = "On the Automorphisms of a Rank One Deligne-Hitchin Moduli Space",
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-K{\"a}hler 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",
author = "Indranil Biswas and Sebastian Heller",
note = "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. ",
year = "2017",
month = sep,
day = "6",
doi = "10.48550/arXiv.1704.04924",
language = "English",
volume = "13",
journal = "Symmetry, Integrability and Geometry: Methods and Applications",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

Download

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 -