Reversible linear differential equations

Details Reversible linear differential equations Reversible linear differential equations

2008-05-30

arxiv.org/abs/0805.4649v8

Mathematics

Algebraic Geometry

16 pages v2 minor changes v3 minor changes v4 major conceptual changes v5 minor changes v6 major conceptual changes v7 an impo

Scientific paper

Let $\nabla$ be a meromorphic connection on a vector bundle over a compact Riemann surface $\Gamma$. An automorphism $\sigma:\Gamma\to\Gamma$ is called a symmetry of $\nabla$ if the pull-back bundle and the pull-back connection can be identified with $\nabla$. We study the symmetries by means of what we call the Fano Group; and, under the hypothesis that $\nabla$ has a unimodular reductive Galois group, we relate the differential Galois group, the Fano group and the symmetries by means of an exact sequence.

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