Connectivity via nongeneric pencils

Mihai Tibar (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We use slicing by nongeneric pencils of hypersurfaces and prove a new theorem of Lefschetz type for singular non compact spaces, at the homotopy level. As applications, we derive results on the topology of the fibres of polynomial functions or the topology of complements of hypersurfaces in $\mathbb C^n$.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Mihai Tibar. Connectivity via nongeneric pencils. International Journal of Mathematics, 2002, 13, pp.111-123. ⟨hal-00022929⟩