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SIGMA 3 (2007), 082, 31 pages arXiv:0708.2186
https://doi.org/10.3842/SIGMA.2007.082
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
Received March 22, 2007, in final form August 06, 2007; Published online August 16, 2007
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.
Key words:
elliptic curve; ramified covering; logarithmic connection; bielliptic curve; genus-2 curve; monodromy; Riemann-Hilbert problem; differential Galois group; elementary transformation; stable bundle; vector bundle.
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