Multivariable Alexander invariants of hypersurface complements

Multivariable Alexander Invariants of Hypersurface Complements

We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin’s vanishing theorem for perverse sheaves. We conclude with explicit computations of twisted cohomology following an idea already exploited in the hyperplane arrangement case, which combines the degen...

On the Alexander invariants of hypersurface complements

Intersection Homology and Alexander Modules of Hypersurface Complements

Let V be a degree d, reduced hypersurface in CP, n ≥ 1, and fix a generic hyperplane, H. Denote by U the (affine) hypersurface complement, CP−V ∪H, and let U be the infinite cyclic covering of U corresponding to the kernel of the linking number homomorphism. Using intersection homology theory, we give a new construction of the Alexander modules Hi(U ;Q) of the hypersurface complement and show t...

Ja n 20 02 HYPERSURFACE COMPLEMENTS , ALEXANDER MODULES AND MONODROMY

L–betti Numbers of Hypersurface Complements

In [DJL07] it was shown that if A is an affine hyperplane arrangement in Cn, then at most one of the L2–Betti numbers b i (C n \ A, id) is non–zero. In this note we prove an analogous statement for complements of complex affine hypersurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of [FLM09, LM06] about L2–Betti numbers of pl...