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A bound on the multiplicity of horizontal sections for a connection on a Riemann surface
Authors:Claire Moura
Institution:Laboratoire de Mathematiques E. Picard, UFR MIG, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
Abstract:We address the question of bounding the multiplicity of the solutions of a linear differential system, setting the problem in invariant terms. A meromorphic connection is considered on a holomorphic vector bundle over a compact Riemann surface. We produce an upper bound on the order of vanishing of an arbitrary horizontal section, which depends only on global data, provided the connection has only regular singularities or the underlying monodromy is irreducible.
Keywords:Meromorphic connection  Multiplicity  Monodromy representation  Regular singularity
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