Nash Problem for quotient surface singularities

We give an affirmative answer to Nash Problem for quotient surface singularities, in particular for the icosahedral singularity $E_8$.Comment: 25 pages with 5 figures. This is part of the author\'s PhD thesi

The Local Nash problem on arc families of singularities

This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.Comment: to appear in Annales de l'Institute Fourie

The space of arcs of an algebraic variety

The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.Comment: 29 pages; v3 corrects some typos. To appear in the Proceedings of the 2015 Summer Institute on Algebraic Geometr