Arc spaces of cA_1 singularities

Publication date: 20 July 2012

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 x^2+y^2+z^2+t^5=0. Version 2: Several small corrections.

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Singularities of surfaces or higher-dimensional varieties (14J17) Local complex singularities (32S05) Arcs and motivic integration (14E18)

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