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arXiv · 1404.0762

Terminal valuations and the Nash problem

Tommaso de Fernex·Roi Docampo
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Abstract

Let X be an algebraic variety of characteristic zero. Terminal valuations are defined in the sense of the minimal model program, as those valuations given by the exceptional divisors on a minimal model over X. We prove that every terminal valuation over X is in the image of the Nash map, and thus it corresponds to a maximal family of arcs through the singular locus of X. In dimension two, this result gives a new proof of the theorem of Fernández de Bobadilla and Pe Pereira stating that, for surfaces, the Nash map is a bijection.

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Tommaso de Fernex, Roi Docampo. 2015-04-13. Terminal valuations and the Nash problem. https://doi.org/10.1007/s00222-015-0597-5

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