Rational Homology Manifolds and Hypersurface Normalizations

We prove a criterion for determining whether the normalization of a complex analytic space—on which the shifted constant sheaf is perverse—is a rational homology manifold, using a perverse sheaf known as the multiple-point complex. This sheaf, naturally associated to such spaces, has notable connections to Milnor monodromy and mixed Hodge modules.

Proceedings of the American Mathematical Society, Volume 147, Pages 1605–1613