Speaker: Guillermo Peñafort Sanchis (University of Valencia)

Title: Open problems about deformations of singular holomorphic map germs

Abstract:

The theory of deformations of germs of holomorphic mappings and the theory of deformations of germs of complex hypersurfaces share many features, which become apparent once one knows how to translate from one to the other. But, for any result about hypersurfaces, the corresponding result about mappings tends to be much harder to prove. In this talk we will discuss open problems about singular mappings, based on the following known results about isolated hypersurface singularities:

· The Milnor number is greater than or equal to the Tjurina number and their quotient cannot exceed the dimension of the ambient space.

· If two hypersurfaces have the same topological type, then their Milnor numbers are equal.

· Singularities cannot be split in two without giving rise to non-trivial homology.