Monodromy of a Class of Logarithmic Connections on an Elliptic Curve
The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their monodromy, differential Galois group and the underlying rank-2 vect...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147230 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve / Francois-Xavier Machu // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862714120377204736 |
|---|---|
| author | Machu, Francois-Xavier |
| author_facet | Machu, Francois-Xavier |
| citation_txt | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve / Francois-Xavier Machu // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their monodromy, differential Galois group and the underlying rank-2 vector bundle. The latter is described in terms of elementary transforms. The question of its (semi)-stability is addressed.
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| first_indexed | 2025-12-07T17:48:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147230 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:48:24Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Machu, Francois-Xavier 2019-02-13T19:33:37Z 2019-02-13T19:33:37Z 2007 Monodromy of a Class of Logarithmic Connections on an Elliptic Curve / Francois-Xavier Machu // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 19 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 14D21; 14H52; 14H60; 32S40 https://nasplib.isofts.kiev.ua/handle/123456789/147230 The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their monodromy, differential Galois group and the underlying rank-2 vector bundle. The latter is described in terms of elementary transforms. The question of its (semi)-stability is addressed. I am greatly indebted to my research advisor D. Markushevich for his encouragement and help. I would like to thank D. Korotkin for explaining me some points. I also acknowledge with pleasure the hospitality of the Mathematics Institute of the Chinese Academy of Sciences, where was done a part of the work on the article. The work was partially supported by the Conseil Departemental du Nord. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Monodromy of a Class of Logarithmic Connections on an Elliptic Curve Article published earlier |
| spellingShingle | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve Machu, Francois-Xavier |
| title | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve |
| title_full | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve |
| title_fullStr | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve |
| title_full_unstemmed | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve |
| title_short | Monodromy of a Class of Logarithmic Connections on an Elliptic Curve |
| title_sort | monodromy of a class of logarithmic connections on an elliptic curve |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147230 |
| work_keys_str_mv | AT machufrancoisxavier monodromyofaclassoflogarithmicconnectionsonanellipticcurve |