Terminal valuations and the Nash problem

• 成果类型: Article
• 署名作者: de Fernex, Tommaso; Docampo, Roi
• 署名单位: Utah System of Higher Education; University of Utah; Universidade Federal Fluminense
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0597-5
• 发表日期: 2016
• 页码: 303-331
• 关键词: arc families; VARIETIES; SPACES; germs; image

摘要

Let 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 . We prove that every terminal valuation over is in the image of the Nash map, and thus it corresponds to a maximal family of arcs through the singular locus of . In dimension two, this result gives a new proof of the theorem of Fernandez de Bobadilla and Pe Pereira stating that, for surfaces, the Nash map is a bijection.