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Oblique poles of $\int_X| {f}| ^{2\lambda}| {g}|^{2\mu} \square$

Publication date2009
Abstract

Existence of oblique polar lines for the meromorphic extension of the current valued function $\int |f|^{2\lambda}|g|^{2\mu}\square$ is given under the following hypotheses: $f$ and $g$ are holomorphic function germs in $\CC^{n+1}$ such that $g$ is non-singular, the germ $S:=\ens{\d f\wedge \d g =0}$ is one dimensional, and $g|_S$ is proper and finite. The main tools we use are interaction of strata for $f$ (see \cite{B:91}), monodromy of the local system $H^{n-1}(u)$ on $S$ for a given eigenvalue $\exp(-2i\pi u)$ of the monodromy of $f$, and the monodromy of the cover $g|_S$. Two non-trivial examples are completely worked out.

Classification
  • arxiv : math.AG
NoteTexte publié dans les actes de la conférence "Complex analysis : several complex variables and connections with PDE theory and geometry", Fribourg (Suisse), 2008. Birkhäuser, 2010, p. 1-23
Citation (ISO format)
BARLET, Daniel, MAIRE, Henri Michel. Oblique poles of $\int_X| {f}| ^{2\lambda}| {g}|^{2\mu} \square$. 2009.
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