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 Ei. The Nash map associates to each irreducible component Ck of the space of arcs through 0 on S the unique component of E cut by the strict transform of the generic arc in Ck. 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.Ei <0 for any i.
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