Details
| Original language | English |
|---|---|
| Pages (from-to) | 241-262 |
| Number of pages | 22 |
| Journal | Manuscripta mathematica |
| Volume | 171 |
| Issue number | 1-2 |
| Early online date | 12 Feb 2022 |
| Publication status | Published - May 2023 |
Abstract
The twistor space of the moduli space of solutions of Hitchin’s self-duality equations can be identified with the Deligne-Hitchin moduli space of λ-connections. We use real projective structures on Riemann surfaces to prove the existence of new components of real holomorphic sections of the Deligne-Hitchin moduli space. Applying the twistorial construction we show the existence of new hyper-Kähler manifolds associated to any compact Riemann surface of genus g≥ 2. These hyper-Kähler manifolds can be considered as moduli spaces of (certain) singular solutions of the self-duality equations.
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In: Manuscripta mathematica, Vol. 171, No. 1-2, 05.2023, p. 241-262.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Real projective structures on Riemann surfaces and new hyper-Kähler manifolds
AU - Heller, Sebastian
N1 - Funding Information: The author thanks Jörg Teschner for first pointing us to (integral) grafting of Fuchsian projective structures, and its interpretation as constant curvature -1 metrics with singularities on compact Riemann surfaces. The authors thanks the referees for helpful comments. The author also thanks the DFG for financial support through the research training group RTG 1670.
PY - 2023/5
Y1 - 2023/5
N2 - The twistor space of the moduli space of solutions of Hitchin’s self-duality equations can be identified with the Deligne-Hitchin moduli space of λ-connections. We use real projective structures on Riemann surfaces to prove the existence of new components of real holomorphic sections of the Deligne-Hitchin moduli space. Applying the twistorial construction we show the existence of new hyper-Kähler manifolds associated to any compact Riemann surface of genus g≥ 2. These hyper-Kähler manifolds can be considered as moduli spaces of (certain) singular solutions of the self-duality equations.
AB - The twistor space of the moduli space of solutions of Hitchin’s self-duality equations can be identified with the Deligne-Hitchin moduli space of λ-connections. We use real projective structures on Riemann surfaces to prove the existence of new components of real holomorphic sections of the Deligne-Hitchin moduli space. Applying the twistorial construction we show the existence of new hyper-Kähler manifolds associated to any compact Riemann surface of genus g≥ 2. These hyper-Kähler manifolds can be considered as moduli spaces of (certain) singular solutions of the self-duality equations.
UR - http://www.scopus.com/inward/record.url?scp=85124733347&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1906.10350
DO - 10.48550/arXiv.1906.10350
M3 - Article
AN - SCOPUS:85124733347
VL - 171
SP - 241
EP - 262
JO - Manuscripta mathematica
JF - Manuscripta mathematica
SN - 0025-2611
IS - 1-2
ER -