Adam PARUSINSKI – Zariski’s dimensionality type. Case of dimensionality type two

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Date(s) - 28/11/2019
13 h 30 min - 14 h 30 min


Adam PARUSINSKI (Laboratoire J. A. Dieudonné, Université Nice Sophia-Antipolis)

In 1979 O. Zariski proposed a general theory of equisingularity for algebraic or algebroid hypersurfaces over an algebraically closed field of characteristic zero. It is based on the notion of dimensionality type that is defined recursively by considering the discriminants loci of subsequent « generic » projections. The singularities of dimensionality type 1 are isomorphic to the equisingular families of plane curve singularities.

In this talk we consider the case of dimensionality type 2, the Zariski equisingular families of surface singularities in 3-space. Using an approach going back to Briançon and Henry, we show that in this case generic linear projections are generic in the sense of Zariski (this is still open for dimensionality type greater than 2). Over the field of complex numbers, we show that such families are bi-Lipschitz trivial, by construction of an explicit Lipschitz stratification. (Based on joint work with L. Paunescu.)

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