Tangential Alexander polynomials and non-reduced degeneration

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

We introduce a notion of tangential Alexander polynomials for plane curves
and study the relation with $\theta$^Alexander polynomial. As an application,
we use these polynomials to study a non-reduced degeneration $C_t \to D_0+jL$.
We show that there exists a certain surjectivity of the fundamental groups and
divisibility among their Alexander polynomials.

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