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unige:11957 
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Oblique poles of $\int_X| {f}| ^{2\lambda}| {g}|^{2\mu} \square$ |
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| Authors | ||
| Year | 2009 | |
| 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. | |
| Identifiers | arXiv: 0901.3070v1 | |
| Note | Texte 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 | |
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| Citation (ISO format) | BARLET, Daniel, MAIRE, Henri Michel. Oblique poles of $\int_X| {f}| ^{2\lambda}| {g}|^{2\mu} \square$. 2009. https://archive-ouverte.unige.ch/unige:11957 |
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