Abstract
Existence of oblique polar lines for the meromorphic extension of the current valued function ∫|f|2λ|g|2μ□ is given under the following hypotheses: f and g are holomorphic function germs in ℂn+1 such that g is non-singular, the germ Σ := {df ∧ dg = 0} is one dimensional, and g is proper and finite on S := {df = 0}. The main tools we use are interaction of strata for f (see [4]), monodromy of the local system H n-1 (u) on S for a given eigenvalue exp(−2iπu) of the monodromy of f, and the monodromy of the cover gS. Two non-trivial examples are completely worked out.
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Barlet, D., Maire, HM. (2010). Oblique Polar Lines of ∫ X |f|2λ|g|2μ□. In: Complex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0009-5_1
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DOI: https://doi.org/10.1007/978-3-0346-0009-5_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0008-8
Online ISBN: 978-3-0346-0009-5
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