Linear components of the tangent cone in the Nash modification of a complex surface singularity

Jawad Snoussi

Journal of Singularities
volume 3 (2011), 83-88

Received: 15 December 2010. Received in revised form: 28 March 2011.

DOI: 10.5427/jsing.2011.3e

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We prove that each linear component of the tangent cone of a complex surface singularity corresponds to at least one singular point in the normalized Nash modification, whenever the minimal resolution factors through the blow-up of the origin of the germ. We give an example of a surface whose tangent cone has no linear component and the normalized Nash modification is singular.

Author(s) information:

Jawad Snoussi
Instituto de Matemáticas, Unidad Cuernavaca
Universidad Nacional Autónoma de México