dc.identifier.uri |
http://dx.doi.org/10.15488/10557 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/10634 |
|
dc.contributor.author |
Beck, Florian
|
|
dc.contributor.author |
Heller, Sebastian
|
|
dc.contributor.author |
Röser, Markus
|
|
dc.date.accessioned |
2021-03-17T13:48:23Z |
|
dc.date.available |
2021-03-17T13:48:23Z |
|
dc.date.issued |
2021 |
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dc.identifier.citation |
Beck, F.; Heller, S.; Röser, M.: Energy of sections of the Deligne–Hitchin twistor space. In: Mathematische Annalen 380 (2021), S. 1169-1214. DOI: https://doi.org/10.1007/s00208-020-02042-0 |
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dc.description.abstract |
We study a natural functional on the space of holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We show that the energy is the residue of the pull-back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. As a byproduct, we show the existence of a hyper-Kähler potentials for new components of real holomorphic sections of twistor spaces of hyper-Kähler manifolds with rotating S1-action. Additionally, we prove that for a certain class of real holomorphic sections of the Deligne–Hitchin moduli space, the energy functional is basically given by the Willmore energy of corresponding equivariant conformal map to the 3-sphere. As an application we use the functional to distinguish new components of real holomorphic sections of the Deligne–Hitchin moduli space from the space of twistor lines. © 2020, The Author(s). |
eng |
dc.language.iso |
eng |
|
dc.publisher |
Heidelberg : Springer |
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dc.relation.ispartofseries |
Mathematische Annalen 380 (2021) |
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dc.rights |
CC BY 4.0 Unported |
|
dc.rights.uri |
https://creativecommons.org/licenses/by/4.0/ |
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dc.subject |
Hyper-Kähler and quaternionic Kähler geometry |
eng |
dc.subject |
Twistor methods in differential geometry |
eng |
dc.subject |
Differential geometric aspects of harmonic maps |
eng |
dc.subject |
Vector bundles on curves and their moduli |
eng |
dc.subject |
Relationships between algebraic curves and integrable systems |
eng |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
Energy of sections of the Deligne–Hitchin twistor space |
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dc.type |
Article |
|
dc.type |
Text |
|
dc.relation.essn |
1432-1807 |
|
dc.relation.issn |
0025-5831 |
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dc.relation.doi |
https://doi.org/10.1007/s00208-020-02042-0 |
|
dc.bibliographicCitation.volume |
380 |
|
dc.bibliographicCitation.firstPage |
1169 |
|
dc.bibliographicCitation.lastPage |
1214 |
|
dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
|