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 $\Sigma$, and moreover determine the ranks of the nontrivial homology groups. These two groups depend on the monodromy at special points of $\Sigma$ and on the effect of the monodromy of the local system over its complement.