Vanishing cycles of pencils of hypersurfaces

We prove an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, and show that the module of vanishing cycles is generated by the images of certain variation maps.Comment: 14 p, more references added, Introduction and Abstract reformulated; based on the Newton Institute preprint NI0102

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.Comment: 17 p.; based on the Newton Institute preprint NI01029, June 200

Milnor Fibre Homology via Deformation

In case of one-dimensional singular locus, we use deformations in order to get refined information about the Betti numbers of the Milnor fibre.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1411.264