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This article is cited in 7 scientific papers (total in 7 papers)
Monodromy of a Class of Logarithmic Connections on an Elliptic Curve
Francois-Xavier Machu Mathématiques - bât. M2, Université Lille 1, F-59655 Villeneuve d'Ascq Cedex, France
Abstract:
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.
Keywords:
elliptic curve; ramified covering; logarithmic connection; bielliptic curve; genus-2 curve; monodromy; Riemann–Hilbert problem; differential Galois group; elementary transformation; stable bundle; vector bundle.
Received: March 22, 2007; in final form August 6, 2007; Published online August 16, 2007
Citation:
Francois-Xavier Machu, “Monodromy of a Class of Logarithmic Connections on an Elliptic Curve”, SIGMA, 3 (2007), 082, 31 pp.
Linking options:
https://www.mathnet.ru/eng/sigma208 https://www.mathnet.ru/eng/sigma/v3/p82
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Abstract page: | 274 | Full-text PDF : | 48 | References: | 32 |
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