Monodromy of a Class of Logarithmic Connections on an Elliptic Curve

Details Monodromy of a Class of Logarithmic Connections on an Elliptic Curve Monodromy of a Class of Logarithmic Connections on an Elliptic Curve

2007-08-16

arxiv.org/abs/0708.2186v1

SIGMA 3 (2007), 082, 31 pages

Mathematics

Algebraic Geometry

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2007.082

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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