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

Camille Plenat; Patrick Popescu-Pampu

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

Camille Plenat·Patrick Popescu-Pampu

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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.

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BibTeX RIS

Camille Plenat, Patrick Popescu-Pampu. 2006-05-24. A class of non-rational surface singularities with bijective Nash map. https://arxiv.org/abs/math/0410145

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