Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1
Holomorphic vector bundles on ℂ × , a complex manifold, with meromorphic connections with poles of Poincaré rank 1 along {0} × , arise naturally in algebraic geometry. They are called ()-structures here. This paper takes an abstract point of view. It gives a complete classification of all ()-struct...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211445 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1. Claus Hertling. SIGMA 17 (2021), 082, 73 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862647226485964800 |
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| author | Hertling, Claus |
| author_facet | Hertling, Claus |
| citation_txt | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1. Claus Hertling. SIGMA 17 (2021), 082, 73 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Holomorphic vector bundles on ℂ × , a complex manifold, with meromorphic connections with poles of Poincaré rank 1 along {0} × , arise naturally in algebraic geometry. They are called ()-structures here. This paper takes an abstract point of view. It gives a complete classification of all ()-structures of rank 2 over germs (, ⁰) of manifolds. In the case of , they separate into four types. Those of the three types have universal unfoldings; those of the fourth type (the logarithmic type) do not. The classification of unfoldings of ()-structures of the fourth type is rich and interesting. The paper finds and lists all ()-structures which are basic in the following sense: Together they induce all rank 2 ()-structures, and each of them is not induced by any other ()-structure in the list. Their base spaces turn out to be 2-dimensional F-manifolds with Euler fields. The paper also provides a classification of all rank 2 ()-structures over it. Also, this classification is surprisingly rich. The backbone of the paper is normal forms. Though also the monodromy and the geometry of the induced Higgs fields and of the base spaces are important and are considered.
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| first_indexed | 2026-03-15T12:06:11Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211445 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T12:06:11Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
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| spelling | Hertling, Claus 2026-01-02T08:35:38Z 2021 Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1. Claus Hertling. SIGMA 17 (2021), 082, 73 pages 1815-0659 2020 Mathematics Subject Classification: 34M56; 34M35; 53C07 arXiv:2009.14314 https://nasplib.isofts.kiev.ua/handle/123456789/211445 https://doi.org/10.3842/SIGMA.2021.082 Holomorphic vector bundles on ℂ × , a complex manifold, with meromorphic connections with poles of Poincaré rank 1 along {0} × , arise naturally in algebraic geometry. They are called ()-structures here. This paper takes an abstract point of view. It gives a complete classification of all ()-structures of rank 2 over germs (, ⁰) of manifolds. In the case of , they separate into four types. Those of the three types have universal unfoldings; those of the fourth type (the logarithmic type) do not. The classification of unfoldings of ()-structures of the fourth type is rich and interesting. The paper finds and lists all ()-structures which are basic in the following sense: Together they induce all rank 2 ()-structures, and each of them is not induced by any other ()-structure in the list. Their base spaces turn out to be 2-dimensional F-manifolds with Euler fields. The paper also provides a classification of all rank 2 ()-structures over it. Also, this classification is surprisingly rich. The backbone of the paper is normal forms. Though also the monodromy and the geometry of the induced Higgs fields and of the base spaces are important and are considered. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 242588615. I would like to thank Liana David for a lot of joint work on (TE)-structures. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 Article published earlier |
| spellingShingle | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 Hertling, Claus |
| title | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 |
| title_full | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 |
| title_fullStr | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 |
| title_full_unstemmed | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 |
| title_short | Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1 |
| title_sort | rank 2 bundles with meromorphic connections with poles of poincaré rank 1 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211445 |
| work_keys_str_mv | AT hertlingclaus rank2bundleswithmeromorphicconnectionswithpolesofpoincarerank1 |