Meromorphic Connections on ℙ1 and the Multiplicity of Abelian Integrals

Movasati, Hossein

doi:10.1007/s10450-006-0381-3

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2006

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“…We suggest an intrinsic version of the main result of [7], motivated by Movasati's work [9] . The object of our study is a horizontal section for a given meromorphic connection living on a compact Riemann surface.…”

Section: Introductionmentioning

confidence: 98%

A bound on the multiplicity of horizontal sections for a connection on a Riemann surface

Moura

2006

Journal of Differential Equations

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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.

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Section: Introductionmentioning

confidence: 98%