Intersection Homology and Alexander Modules of Hypersurface Complements
نویسنده
چکیده
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 that, if i ≤ n, these are torsion over the ring of rational Laurent polynomials. We also obtain obstructions on the associated global polynomials. Their zeros are roots of unity of order d and are entirely determined by the local topological information encoded by the link pairs of singular strata of a stratification of the pair (CP, V ). As an application, we give obstructions on the eigenvalues of monodromy operators associated to the Milnor fibre of a projective hypersurface arrangement.
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