Abstract
We construct an infinite series of equisingular families of projective plane curves with ordinary multiple points such that each family has irreducible components of different dimensions. This phenomenon has been unknown for curves with ordinary multiple points and disproves some wrong expectations about such curves. We observe also that, for each family, the fundamental groups of the complement of curves in different components coincide (and are abelian). The examples are compared with sufficient irreducibility conditions for equisingular families of plane curves in order to get limits of possible improvements for such sufficient conditions.
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