Publication: Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities
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2007
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Oxford University Press
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Abstract
In this paper we give a positive answer to a question of Nash, concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii.
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Alexeev, V. "Complete Moduli in the Presence of Semiabelian Group Action." Annals of Mathematics 2 155, no. 3 (2002): 611–708.
Abhyankar, S. S. "On the Ramification of Algebraic Functions." American Journal of Mathematics 77 (1955): 575–592.
Bouvier, C. "Diviseurs Essentiels, Composantes Essentielles des Variétés Toriques Singulères." Duke Mathematical Journal 91, no. 3 (1998): 609–620.
Bouvier, C., and G. Gonzalez-Sprinberg. "Système Générateur Minimal, Diviseurs Essentiels et G-Désingularisations de Variétés Toriques." Tôhoku Mathematical Journal 47 (1995): 125–149.
Denef, J., and F. Loeser. "Germs of Arcs on Singular Algebraic Varieties and Motivic Integration." Inventiones Mathematicae 135, no. 1 (1999): 201–232.
Fulton, W. Introduction to Toric Varieties, Annals of Mathematics Studies, 131. Princeton, New Jersey: Princeton University Press, 1993.
Gau, Y.-N. "Embedded Topological Classification of Quasi-Ordinary Singularities." Memoirs of the American Mathematical Society 388 (1988): 109–127.
González Pérez, P. D. "Singularités Quasi-Ordinaires Toriques et Polyèdre de Newton du Discriminant." Canadian Journal of Mathematics 52, no. 2 (2000): 348–368.
González Pérez, P. D. "Toric Embedded Resolutions of Quasi-Ordinary Hypersurface Singularities." Annales de L'Institut Fourier (Grenoble) 53, no. 6 (2003): 1819–1881.
González Pérez, P. D., and F. Hernando. "Quasi-Ordinary Singularities, Essential Divisors and Poincaré Series." (2007): Preprint arXiv: 0705.0603 [math.AG].
Ishii, S., and J. Kollar. "The Nash Problem On Arc Families of Singularities." Duke Mathematical Journal 120, no. 3 (2003): 601–620.
Ishii, S. "The Arc Space of a Toric Variety." Journal of Algebra 278, no. 2 (2004): 666–683.
Ishii, S. "Arcs, Valuations and the Nash Map." Journal Fur Die Reine Und Angewandte Mathematik 588 (2005): 71–92.
Ishii, S. "The Local Nash problem On Arc Families of Singularities." Annales de L'Institut Fourier (Grenoble) 56, no. 4 (2006): 1207–1224.
Jung, H. W. E. "Darstellung der Funktionen Eines Algebraischen Körpers Zweier Unabhaängigen Veränderlichen x, y in der Umgebung Einer Stelle x=a, y=b." Journal Fur Die Reine Und Angewandte Mathematik 133 (1908): 289–314.
Lejeune-Jalabert, M., and A. Reguera López. "Arcs and Wedges On Sandwiched Surface Singularities." American Journal of Mathematics 121, no. 6 (1999): 1191–1213.
Lipman, J. "Introduction to Resolution of Singularities" Pp. 187-230 in Proceedings of Symposia in Pure Mathematics, 29. Providence, RI American Mathematical Society, 1975.
Lipman, J. Pp. 1-107 in Topological Invariants of Quasi-Ordinary Singularities, 388. Providence, RI: American Mathematical Society, 1988.
Morales, M. "The Nash Problem on Arcs for Surface Singularities." (2006): Preprint arXiv:math/0609629.
Nash, J. F. Jr. "Arc Structure of Singularities, A celebration of John F. Nash, Jr." Duke Mathematical Journal 81, no. 1 (1995): 31–38.
Oda, T. "Convex Bodies and Algebraic Geometry." Annals of Mathematics Studies, Vol. 131. Berlin: Springer-Verlag, 1988.
Petrov, P. "Nash Problem for Stable Toric Varieties." Mathematische Nachrichten, (forthcoming); (2006): Preprint arXiv: math.AG/0604432.
Plénat, C. "À propos du Problème des Arcs de Nash." Annales de L'Institut Fourier (Grenoble) 55, no. 3 (2005): 805–823.
Plénat, C. "Résolution du Problème des Arcs de Nash Pour Les Points Doubles Rationnels Dn." C. R. Acad. Sci. Paris, Ser. 1 340, no. 10 (2005): 747–750.
Plenat, C., and P. Popescu-Pampu. "A Class of Non-Rational Surface Singularities with Bijective Nash Map." Bulletin De La Societe Mathematique De France 134, no. 3 (2006): 383–394.
Plenat C., and P. Popescu-Pampu. "Families of Higher Dimensional Germs with Bijective Nash Map." (2006): Preprint Arxiv math.AG/0605566.
Popescu-Pampu, P. "On the Analytical Invariance of the Semigroups of a Quasi-Ordinary Hypersurface Singularity." Duke Mathematical Journal 124, no. 1 (2004): 67–104.
Reguera-Lopez, A. J. "Families of Arcs On Rational Surface Singularities." Manuscripta Mathematica 88 (1995): 321–333.
Reguera-Lopez, A. J. "Image of the Nash Map in Terms of Wedges." C. R. Acad. Sci. Paris, Ser. 1 338, no. 5 (2004): 385–390.