On linear differential equations with reductive Galois group

Details On linear differential equations with reductive Galois group On linear differential equations with reductive Galois group

2010-07-26

arxiv.org/abs/1007.4502v3

Mathematics

Algebraic Geometry

v2 information on funding added v3 presentation rewritten, computational examples added

Scientific paper

Given a connection on a meromorphic vector bundle over a compact Riemann surface with reductive Galois group, we associate to it a projective variety. Connections such that their associated projective variety are curves can be classified, up to projective equivalence, using ruled surfaces. In particular, such a meromorphic connection is the pullbacks of a Standard connection. This extend a similar result by Klein for second-order ordinary linear differential equations to a broader class of equations.

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