Regular Functions Transversal at Infinity

Abstract

We generalize and complete some of Maxim's recent results on Alexander invariants of a polynomial transversal to the hyperplane at infinity. Roughly speaking, and surprisingly, such a polynomial behaves both topologically and algebraically (e.g. in terms of the variation of MHS on the cohomology of its smooth fibers), like a homogeneous polynomial.

This is a substantial improvement of the paper "Alexander Invariants and Transversality" by the first author, see math.AG/0411329. Both the topology and the associated mixed Hodge structures (not touched in the previous paper) are clearly described