The Nash problem of arcs and the rational double points
- [1] Université de Provence LATP UMR 6632 Centre de Mathématiques et Informatique 39 rue Joliot-Curie 13453 Marseille cedex 13 (France)
Annales de l’institut Fourier (2008)
- Volume: 58, Issue: 7, page 2249-2278
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topReferences
top- M. Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129-136 Zbl0142.18602MR199191
- C. Bouvier, Diviseurs essentiels, composantes essentielles des variétés toriques singulières, Duke Math. J. 91 (1998), 609-620 Zbl0966.14038MR1604179
- C. Bouvier, G. Gonzales-Sprinberg, Système générateur minimal, diviseurs essentiels et G-désingularisations de varitétés toriques, Tohoku Math. J. 47 (1995), 125-149 Zbl0823.14006MR1311446
- D. Eisenbud, Commutative Algebra with a view toward Algebraic Geometry, 150 (1995), Springer-Verlag, New York Zbl0819.13001MR1322960
- J. Fernandez-Sanchez, Equivalence of the Nash conjecture for primitive and sandwiched singularities, Proc. Amer. Math. Soc. 133 (2005), 677-679 Zbl1056.14004MR2113914
- S. Ishii, Arcs, valuations and the Nash map, arXiv: math.AG/0410526 Zbl1082.14007
- S. Ishii, The local Nash problem on arc families of singularities, arXiv: math.AG/0507530 Zbl1116.14030
- S. Ishii, J. Kollár, The Nash problem on arc families of singularities, Duke Math. J. 120, 3 (2003), 601-620 Zbl1052.14011MR2030097
- M. Lejeune–Jalabert, Arcs analytiques et résolution minimale des singularités des surfaces quasi-homogènes, Séminaire sur les Singularités des Surfaces, Lecture Notes in Math. 777 (1980), 303-336, Springer-Verlag Zbl0432.14020
- M. Lejeune–Jalabert, Désingularisation explicite des surfaces quasi-homogènes dans , Nova Acta Leopoldina NF 52, Nr 240 (1981), 139-160 Zbl0474.14021MR642702
- M. Lejeune–Jalabert, Courbes tracées sur un germe d’hypersurface, Amer. J. Math. 112 (1990), 525-568 Zbl0743.14002
- M. Lejeune–Jalabert, A. Reguera, Arcs and wedges on sandwiched surface singularities, Amer. J. Math. 121 (1999), 1191-1213 Zbl0960.14015MR1719822
- H. Matsumura, Commutative ring theory. Translated from the Japanese by M. Reid, 8 (1986), Cambridge University Press, Cambridge Zbl0603.13001MR879273
- J. F. Jr. Nash, Arc structure of singularities, A celebration of John F. Nash, Jr. Duke Math. J. 81, 1 (1995), 31-38 Zbl0880.14010MR1381967
- C. Plénat, A propos du problème des arcs de Nash, Annales de l’Institut Fourier 55 (2005), 805-823 Zbl1080.14021
- C. Plénat, Résolution du problème des arcs de Nash pour les points doubles rationnels ., Note C.R.A.S, Série I 340 (2005), 747-750 Zbl1072.14004MR2141063
- C. Plénat, P. Popescu-Pampu, A class of non-rational surface singularities for which the Nash map is bijective, Bulletin de la SMF 134 (2006), 383-394 Zbl1119.14007MR2245998
- A. Reguera, Families of arcs on rational surface singularities, Manuscripta Math 88, 3 (1995), 321-333 Zbl0867.14012MR1359701
- A. Reguera, Image of the Nash map in terms of wedges, C. R. Acad. Sci. Paris, Ser. I 338 (2004), 385-390 Zbl1044.14032MR2057169