Arc spaces of cA₁ singularities

2012/07/20 by Janós Kollár, Kollár, János
Mathematics · #14B05 (Primary) 14J17 #14E15 #14E18 #32S05 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1207.5036

openalex publication_date 2012/07/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let p be a singular point of a complex hypersurface whose tangent cone is a quadric of rank at least 3. We show that the space of arcs through p is irreducible. Using a method of de Fernex, this shows that the Nash problem has a negative answer for x²+y²+z²+t⁵=0. Version 2: Several small corrections.

Related

• Arc spaces of cA-type singularities
• The Nash problem on arc families of singularities
• The Nash problem of arcs and the rational double point E₆
• The space of arcs of an algebraic variety
• Résolution du problème des arcs de Nash pour une famille d'hypersurfaces quasi-rationnelles