The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles

The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold, defined on the total space of a singular torus fibration with one singular nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric should be part of the local model of the hyperkähler metric of the Hitchin mo...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2025
Main Author: Tulli, Iván
Format: Article
Language:English
Published: Інститут математики НАН України 2025
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212886
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles. Iván Tulli. SIGMA 21 (2025), 005, 63 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Tulli, Iván
author_facet Tulli, Iván
citation_txt The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles. Iván Tulli. SIGMA 21 (2025), 005, 63 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold, defined on the total space of a singular torus fibration with one singular nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric should be part of the local model of the hyperkähler metric of the Hitchin moduli spaces, near the most generic kind of singular locus of the Hitchin fibration. In order to relate the Ooguri-Vafa space to the Hitchin moduli spaces, we show that the Ooguri-Vafa space can be interpreted as a set of rank 2, framed wild harmonic bundles over ℂ¹, with one irregular singularity. Along the way, we show that a certain twistor family of holomorphic Darboux coordinates, which describes the hyperkähler geometry of the Ooguri-Vafa space, has an interpretation in terms of Stokes data associated to our framed wild harmonic bundles.
first_indexed 2026-03-21T10:46:13Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2026-03-21T10:46:13Z
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spelling Tulli, Iván
2026-02-13T13:50:57Z
2025
The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles. Iván Tulli. SIGMA 21 (2025), 005, 63 pages
1815-0659
2020 Mathematics Subject Classification: 53C26; 53C28; 34M40
arXiv:1912.00261
https://nasplib.isofts.kiev.ua/handle/123456789/212886
https://doi.org/10.3842/SIGMA.2025.005
The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold, defined on the total space of a singular torus fibration with one singular nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric should be part of the local model of the hyperkähler metric of the Hitchin moduli spaces, near the most generic kind of singular locus of the Hitchin fibration. In order to relate the Ooguri-Vafa space to the Hitchin moduli spaces, we show that the Ooguri-Vafa space can be interpreted as a set of rank 2, framed wild harmonic bundles over ℂ¹, with one irregular singularity. Along the way, we show that a certain twistor family of holomorphic Darboux coordinates, which describes the hyperkähler geometry of the Ooguri-Vafa space, has an interpretation in terms of Stokes data associated to our framed wild harmonic bundles.
I thank Andrew Neitzke for very helpful discussions, support, and for reading the preliminary versions of this paper. I would also like to thank the anonymous referees, who carefully read the paper and gave very useful suggestions and improvements.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
Article
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spellingShingle The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
Tulli, Iván
title The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
title_full The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
title_fullStr The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
title_full_unstemmed The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
title_short The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles
title_sort ooguri-vafa space as a moduli space of framed wild harmonic bundles
url https://nasplib.isofts.kiev.ua/handle/123456789/212886
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