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 , i 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 I.