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.

19 pages, 1 figure, small corrections

References in corpus (2)

• Solvable Groups, Free Divisors and Nonisolated Matrix Singularities II: Vanishing Topology
• Milnor Fibre Homology via Deformation

Cited by in corpus (3)

• The vanishing cohomology of non-isolated hypersurface singularities
• Polar degree of hypersurfaces with 1-dimensional singularities
• Vanishing cohomology and Betti bounds for complex projective hypersurfaces