  In this note we consider the Milnor fiber $F$ associated to a reduced
projective plane curve $C$. A computational approach for the determination of
the characteristic polynomial of the monodromy action on the first cohomology
group of $F$, also known as the Alexander polynomial of the curve $C$, is
presented. This leads to an effective algorithm to detect all the monodromy
eigenvalues and, in many cases, explicit bases for the monodromy eigenspaces in
terms of polynomial differential forms.

Algebraic Geometry