A computational approach to Milnor fiber cohomology

Friday 1 April 2016 from 10:00–11:00 in Carslaw 375

Abstract: In this talk 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.