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
Main Author: Machu, Francois-Xavier
Format: Article
Language:English
Published: Інститут математики НАН України 2007
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
id nasplib_isofts_kiev_ua-123456789-147230
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Monodromy of a Class of Logarithmic Connections on an Elliptic Curve
spellingShingle Monodromy of a Class of Logarithmic Connections on an Elliptic Curve
Machu, Francois-Xavier
title_short 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_sort monodromy of a class of logarithmic connections on an elliptic curve
author Machu, Francois-Xavier
author_facet Machu, Francois-Xavier
publishDate 2007
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147230
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.
work_keys_str_mv AT machufrancoisxavier monodromyofaclassoflogarithmicconnectionsonanellipticcurve
first_indexed 2025-12-07T17:48:24Z
last_indexed 2025-12-07T17:48:24Z
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