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Desingularization of Hypersurfaces Over Fields of Characteristic Zero by Villamayor

Talker: Gábor Bodnár  

Until recently, the most outstanding result in the resolution of singularities was Hironaka's famous proof for existence of desingularization of hypersurfaces over fields of characteristic zero in arbitrary dimension. This proof, however, is not constructive. In 1989, O. Villamayor came up with a constructive version of the proof of Hironaka's theorem. In his paper, through many stages of newly defined objects and by careful distinction between different types of "singular situations" he defines an upper-semicontinuous function, with the property, that by blowing up repeatedly along its maximum stratum, within finitely many steps, one reaches a resolution.

In this talk, we go through the first definitions given by Villamayor, and the main ideas of the proof. Finally we arrive to the definition of the Villamayor stratification function.

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