Nil-manifolds as links of isolated singularities

Richard M. Hain

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We attach a limit mixed Hodge structure to any polynomial map $f : ℂ^{n} \to ℂ$ . The equivariant Hodge numbers of this mixed Hodge structure are invariants of $f$ which reflect its asymptotic behaviour. We compute them for a generic class of polynomials in terms of equivariant Hodge numbers attached to isolated hypersurface singularities and equivariant Hodge numbers of cyclic coverings of projective space branched along a hypersurface. We show how these invariants allow to determine topological invariants...