Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l’irrégularité
Identifieur interne : 000179 ( France/Analysis ); précédent : 000178; suivant : 000180Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l’irrégularité
Auteurs : Yves André [France]Source :
- Inventiones mathematicae [ 0020-9910 ] ; 2007-10-01.
Abstract
Abstract: We prove Malgrange’s conjecture on the absence of confluence phenomena for integrable meromorphic connections. More precisely, if Y→X is a complex-analytic fibration by smooth curves, Z a hypersurface of Y finite over X, and ∇ an integrable meromorphic connection on Y with poles along Z, then the function which attaches to x∈X the sum of the irregularities of the fiber ∇(x) at the points of Z x is lower semicontinuous. The proof relies upon a study of the formal structure of integrable meromorphic connections in several variables.
Url:
DOI: 10.1007/s00222-007-0060-3
Affiliations:
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