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RESIDUES OF HOLOMORPHIC FOLIATIONS RELATIVE TO A GENERAL SUBMANIFOLD

Published online by Cambridge University Press:  01 June 2005

CÉSAR CAMACHO  and
DANIEL LEHMANN
CÉSAR CAMACHO
Affiliation:
Instituto de Matemática Pura e Aplicada (IMPA), 110 Estrada Dona Castorina, Rio de Janeiro, [email protected]
DANIEL LEHMANN
Affiliation:
Département des Sciences Mathématiques, Université de Montpellier II, Place Eugène Bataillon, F-34095 Montpellier Cedex 5, [email protected]
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Abstract

Let $\Cal F$ be a holomorphic foliation (possibly with singularities) on a non-singular manifold $M$, and let $V$ be a complex analytic subset of $M$. Usual residue theorems along $V$ in the theory of complex foliations require that $V$ be tangent to the foliation (that is, a union of leaves and singular points of $V$ and $\Cal F$); this is the case for instance for the blow-up of a non-dicritical isolated singularity. In this paper, residue theorems are introduced along subvarieties that are not necessarily tangent to the foliation, including the blow-up of the dicritical situation.

Keywords

53C1257R2055N15
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 3 , June 2005 , pp. 435 - 445
Copyright
© The London Mathematical Society 2005

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