A class of non-rational surface singularities with bijective Nash map

Camille Plenat (1) , Patrick Popescu-Pampu (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 IMJ - Institut de Mathématiques de Jussieu

Let (S,0) be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor E and its irreducible components E_i. The Nash map associates to each irreducible component C_k of the space of arcs through 0 on S the unique component of E cut by the strict transform of the generic arc in C_k. Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if E.E_i <0 for any i.

Domaines: Géométrie algébrique [math.AG]

Camille Plenat, Patrick Popescu-Pampu. A class of non-rational surface singularities with bijective Nash map. Bulletin de la société mathématique de France, 2006, 134, pp.383-394. ⟨hal-00133190⟩