#### Anne Pichon

Université Aix-Marseille

### Resumen:

Minimal surface singularities, introduced by J. Kollár in 1985, play a key role in resolution theory of surface singularities since they appear as central objects in the two main resolution algorithms : the resolution obtained by a sequence of normalized Nash transformations (Spivakovky, 1990) and the one obtained by successive normalized blow-ups of points (Zariski 1939) as showed by Bondil and Lê in 2002. The question of the existence of a duality between these two algorithms, asserted by D. T. Lê, remains open, and the fact that minimal singularities seem to be the common denominator between them suggests the need of a better understanding of this class of surface germs.

I will present a recent joint work with Walter Neumann and Helge Moller Perdersen in which we show that minimal surface singularities can be characterized by a remarkable metric property among rational surface singularities.

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