Vanishing homology of projective hypersurfaces with 1-dimensional singularities

Abstract

We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus Σ , and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of Σ and on the effect of the monodromy of the local system over its complement.