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On Fuchs' relation for linear differential systems

Published online by Cambridge University Press:  04 December 2007

Eduardo Corel
Eduardo Corel
Affiliation:
Laboratoire AGAT, Université des Sciences et Technologies Lille 1, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex, [email protected] 14, rue Lepic, 75018 Paris, France
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Abstract

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In this paper, we give a formal algebraic notion of exponents for linear differential systems at any singularity as eigenvalues of the residue of a regular connection on a maximal lattice (that we call ‘Levelt's lattice’). This allows us to establish upper and lower bounds for the sum of these exponents for differential systems on ${\mathbb P}^{1}(\mathbb{C})$.

Keywords

differential systemirregular singularityconnectionLevelt latticeexponentsFuchs' relation34A2034A3012H0534C2032S40
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 5 , September 2004 , pp. 1367 - 1398
Copyright
Foundation Compositio Mathematica 2004