In a recent paper, Dimca and Némethi pose the problem of finding a homogeneous polynomial such that the homology of the complement of the hypersurface defined by is torsion-free, but the homology of the Milnor fiber of has torsion. We prove that this is indeed possible, and show by construction that, for each prime , there is a polynomial with –torsion in the homology of the Milnor fiber. The techniques make use of properties of characteristic varieties of hyperplane arrangements.
"Torsion in Milnor fiber homology." Algebr. Geom. Topol. 3 (1) 511 - 535, 2003. https://doi.org/10.2140/agt.2003.3.511