Displaying similar documents to “Bernstein polynomials and spectral numbers for linear free divisors”

Linear free divisors and the global logarithmic comparison theorem

Michel Granger, David Mond, Alicia Nieto-Reyes, Mathias Schulze (2009)

Annales de l’institut Fourier

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A complex hypersurface D in ℂ n is a linear free divisor (LFD) if its module of logarithmic vector fields has a global basis of linear vector fields. We classify all LFDs for n at most 4 . By analogy with Grothendieck’s comparison theorem, we say that the global logarithmic comparison theorem (GLCT) holds for D if the complex of global logarithmic differential forms computes the complex cohomology of ℂ n ∖ D . We develop a general...

Bernstein-Sato Polynomials and Spectral Numbers

Andréa G. Guimarães, Abramo Hefez (2007)

Annales de l’institut Fourier

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In this paper we will describe a set of roots of the Bernstein-Sato polynomial associated to a germ of complex analytic function in several variables, with an isolated critical point at the origin, that may be obtained by only knowing the spectral numbers of the germ. This will also give us a set of common roots of the Bernstein-Sato polynomials associated to the members of a μ -constant family of germs of functions. An example will show that this set may sometimes consist of all common...

Limit currents and value distribution of holomorphic maps

Daniel Burns, Nessim Sibony (2012)

Annales de l’institut Fourier

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We construct d -closed and d d c -closed positive currents associated to a holomorphic map φ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.