Monodromy of a Class of Logarithmic Connections on an Elliptic Curve

被引：6
|
作者：
Machu, Francois-Xavier [1 ]
机构：
[1] Univ Lille 1, F-59655 Villeneuve Dascq, France
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2007年 / 3卷
关键词：
elliptic curve; ramified covering; logarithmic connection; bielliptic curve; genus-2; curve; monodromy; Riemann-Hilbert problem; differential Galois group; elementary transformation; stable bundle; vector bundle;
D O I：
10.3842/SIGMA.2007.082
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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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页数：31
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