# Oblique poles of $int X| {f}| ^{2λ}| {g}|^{2μ} square$ - Mathematics > Algebraic Geometry

Oblique poles of $int X| {f}| ^{2λ}| {g}|^{2μ} square$ - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: Existence of oblique polar lines for the meromorphic extension of the currentvalued function $\int |f|^{2\lambda}|g|^{2\mu}\square$ is given under thefollowing 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 onedimensional, and $g| S$ is proper and finite. The main tools we use areinteraction 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 arecompletely worked out.

Author: Daniel Barlet, H.-M. Maire

Source: https://arxiv.org/