Terminal valuations and the Nash problem

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-04
Main Authors: de Fernex, Tommaso, Docampo, Roi
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1404.0762