Carrousel in family and non-isolated hypersurface singularities in ℂ3

Françoise Michel (1) , Anne Pichon (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 I2M - Institut de Mathématiques de Marseille

We study the boundary L t of the Milnor fiber for the reduced holomorphic germs f : (C 3 , 0) → (C, 0) having a non-isolated singularity at 0. We prove that L t is a graph manifold by using a new technique of carrousel depending on one parameter. Our results enable us to compare the topology of L t and of the link of the normalization of f −1 (0).

Domaines: Géométrie algébrique [math.AG]

Françoise Michel, Anne Pichon. Carrousel in family and non-isolated hypersurface singularities in ℂ3. Journal für die reine und angewandte Mathematik, 2016, 2016 (720), pp.1-32. ⟨10.1515/crelle-2014-0074⟩. ⟨hal-02543406⟩