# monodromy of plane curve singularities

Are there two IRREDUCIBLE plane curve singularities having different equisingular type with the same monodromy (linear action on the first homology group of the (regular) Milnor fibre)?

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In fact, from the theorem of Campillo, Delgado, and Gusein-Zade, one sees that the zeta function of the monodromy -- i.e., the Alexander polynomial divided by $(1-t)$ -- is the Poincaré series of the semigroup of the curve singularity.