Whitney equisingularity of families of surfaces and the Ruas's conjecture.

Resumen:

In this talk, we will speak about families of singular surfaces in C^3 (with non-isolated singularities) parametrized by A-fi nitely determined map germs. We will consider the notions of topological triviality and Whitney equisingularity of an unfolding F of a fi nitely determined map germ f from C^2 to C^3, in others words, we will consider some notions of equisingularity of families of surfaces. Finally, we will talk about the Ruass conjecture and the Zariski multiplicitiy conjecture and some results related.

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