The vanishing cohomology of non-isolated hypersurface singularities
arXiv:2007.07064 · doi:10.1112/jlms.12570
Abstract
We employ the perverse vanishing cycles to show that each reduced cohomology group of the Milnor fiber, except the top two, can be computed from the restriction of the vanishing cycle complex to only singular strata with a certain lower bound in dimension. Guided by geometric results, we alternately use the nearby and vanishing cycle functors to derive information about the Milnor fiber cohomology via iterated slicing by generic hyperplanes. These lead to the description of the reduced cohomology groups, except the top two, in terms of the vanishing cohomology of the nearby section. We use it to compute explicitly the lowest (possibly nontrivial) vanishing cohomology group of the Milnor fiber.
final version, accepted for publication
References in corpus (6)
- The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils
- Images of analytic map germs, and singular fibrations
- Vanishing homology of projective hypersurfaces with 1-dimensional singularities
- Milnor Fibre Homology via Deformation
- Complex monodromy and the topology of real algebraic sets
- Vanishing cohomology and Betti bounds for complex projective hypersurfaces