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 |
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| 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| _version_ | 1862727497240543232 |
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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.
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| first_indexed | 2026-03-21T10:46:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212886 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T10:46:13Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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 published earlier |
| 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 |
| work_keys_str_mv | AT tulliivan theoogurivafaspaceasamodulispaceofframedwildharmonicbundles AT tulliivan oogurivafaspaceasamodulispaceofframedwildharmonicbundles |