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

Abstract

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.

8 pages; compared to the first version, we changed slightly the title in order to make it similar with the title of math.AG/0605566 (where the main theorem 5.1 is generalized to arbitrary dimensions) and we modified remarks 3.2 and 4.2