Hodge numbers attached to a polynomial map

Abstract

Given a polynomial map $f:{\mathbb{C}}^{n+1}\to \mathbb{C}$, one can attach to it a geometrical variation of mixed Hodge structures (MHS) which gives rise to a limit MHS. The equivariant Hodge numbers of this MHS are analytical invariants of the polynomial map and reflect its asymptotic behaviour. In this paper we compute them for a class of generic polynomials, in terms of Hodge numbers attached to isolated hypersurface singularities and Hodge numbers of cyclic coverings of projective space branched along a hypersurface.

AMS-LaTeX, 33 pages