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A family of quai-rational hypersurfaces with bijective Nash map. (Une famille dhypersurfaces quasi-rationnelles avec application de Nash bijective.) (French) Zbl 1221.14017

This paper shows the affirmative answer to the Nash problem for two-dimensional hypersurface singularities of special type including \(E_6\) and \(E_7\). The author also proves that if the Nash map is bijective for a normal surface singularity, then the Nash map is also bijective for the normal singularity obtained by contracting a subdivisor of the exceptional divisor on the minimal resolution.

MSC:

14E18 Arcs and motivic integration
14B05 Singularities in algebraic geometry
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[1] Bouvier, C.; Gonzalez-Sprinberg, G., Système générateur minimal, diviseurs essentiels et G-désingularisations de variétés toriques, Tohoku math. J. ser., 2, 47, 125-149, (1995) · Zbl 0823.14006
[2] Campillo, A.; Gonzalez-Sprinberg, G.; Lejeune-Jalabert, M., Clusters of infinitely near points, Math. ann., 306, 169-194, (1996) · Zbl 0853.14002
[3] Flenner, H.; Zaidenberg, M., Rational curves and rational singularities, Math. Z., 244, 549-575, (2003) · Zbl 1043.14008
[4] Gonzalez-Sprinberg, G.; Lejeune-Jalabert, M., Modèles canoniques plongés I, Kodai math. J., 14, 194-209, (1991) · Zbl 0772.14008
[5] Ishii, S., Jet schemes, arc spaces and the Nash problem, C. R. math. acad. sci. soc. R. can., 29, 1-21, (2007) · Zbl 1162.14006
[6] Morales, M., Some numerical criteria for the Nash problem on arcs for surfaces, Nagoya math. J., 191, 1-19, (2008) · Zbl 1178.14004
[7] Plénat, C.; Popescu-Pampu, P., A class of non-rational surface singularities with bijective Nash map, Bull. soc. math. France, 134, 3, 383-394, (2006) · Zbl 1119.14007
[8] Reguera, A., A curve selection lemma in spaces of arcs and the image of the Nash map, Compos. math., 142, 119-130, (2006) · Zbl 1118.14004
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