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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Bibliographic Details
Main Author:	Francois-Xavier Machu
Format:	Article
Language:	English
Published:	National Academy of Science of Ukraine 2007-08-01
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Subjects:	elliptic curve ramified covering logarithmic connection bielliptic curve genus-2 curve monodromy Riemann-Hilbert problem differential Galois group elementary transformation stable bundle vector bundle
Online Access:	http://www.emis.de/journals/SIGMA/2007/082/

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spelling	doaj-662a72eddb604b00af7f71e26cbf25bc2020-11-24T23:34:55ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-08-013082Monodromy of a Class of Logarithmic Connections on an Elliptic CurveFrancois-Xavier MachuThe 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.http://www.emis.de/journals/SIGMA/2007/082/elliptic curveramified coveringlogarithmic connectionbielliptic curvegenus-2 curvemonodromyRiemann-Hilbert problemdifferential Galois groupelementary transformationstable bundlevector bundle
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Francois-Xavier Machu
spellingShingle	Francois-Xavier Machu Monodromy of a Class of Logarithmic Connections on an Elliptic Curve Symmetry, Integrability and Geometry: Methods and Applications elliptic curve ramified covering logarithmic connection bielliptic curve genus-2 curve monodromy Riemann-Hilbert problem differential Galois group elementary transformation stable bundle vector bundle
author_facet	Francois-Xavier Machu
author_sort	Francois-Xavier Machu
title	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_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
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2007-08-01
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.
topic	elliptic curve ramified covering logarithmic connection bielliptic curve genus-2 curve monodromy Riemann-Hilbert problem differential Galois group elementary transformation stable bundle vector bundle
url	http://www.emis.de/journals/SIGMA/2007/082/
work_keys_str_mv	AT francoisxaviermachu monodromyofaclassoflogarithmicconnectionsonanellipticcurve
_version_	1725527094354509824

Monodromy of a Class of Logarithmic Connections on an Elliptic Curve

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