Geodesic
Linear components of the tangent cone in the Nash modification of a complex surface singularity
Journal of Singularities, Tome 3 (2011), pp. 83-88

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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. 
@article{10_5427_jsing_2011_3e,
     author = {Jawad Snoussi},
     title = {Linear components of the tangent cone in the {Nash} modification of a complex surface singularity},
     journal = {Journal of Singularities},
     pages = {83--88},
     publisher = {mathdoc},
     volume = {3},
     year = {2011},
     doi = {10.5427/jsing.2011.3e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2011.3e/}
}
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Jawad Snoussi. Linear components of the tangent cone in the Nash modification of a complex surface singularity. Journal of Singularities, Tome 3 (2011), pp. 83-88. doi: 10.5427/jsing.2011.3e

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