turkmath.org

(Joint work with H. Mourtada) One of the aim of Nash’ paper on the arcs spaces (1968) was to understand resolutions of singularities via the arcs living on the singular variety; in particular he wanted to give a one to one correspondence between families of arcs and essential exceptionnal divisors. J.Fernandez de Bobadilla and M.Pe Pereira (2011) have shown that such a bijective correspondence for abstract resolutions of singular surfaces. But the proof does not give a constructive way to get the resolution from the arcs space. With H.Mourtada, we construct an embedded toric resolution of simple singularities from their jets schemes. It is the result I will discuss in the talk.