Tangential Alexander polynomials and non-reduced degeneration

Abstract

We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with $θ$^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.