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We study the singularity at the origin of
of an arbitrary homogeneous polynomial in
variables with complex coefficients, by investigating the monodromy characteristic polynomials
as well as the relation between the monodromy zeta function and the Hodge spectrum of the singularity. In the case
, we give a description of
in terms of the multiplier ideal.
We compute the Alexander polynomial of a nonreduced nonirreducible complex projective plane curve with mutually coprime orders of vanishing along its irreducible components in terms of certain multiplier ideals.
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