This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.
Cet article présente la réponse positive au problème du Nash local pour une singularité torique ainsi que pour une singularité analytiquement prétorique. Il en résulte comme corollaire une réponse affirmative au problème du Nash local pour une singularité quasi ordinaire.
Keywords: Arc space, Nash problem, singularities
Mot clés : arc de singularité, problème de Nash, singularité
@article{AIF_2006__56_4_1207_0, author = {Ishii, Shihoko}, title = {The {Local} {Nash} problem on arc families of singularities}, journal = {Annales de l'Institut Fourier}, pages = {1207--1223}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {56}, number = {4}, year = {2006}, doi = {10.5802/aif.2210}, zbl = {1116.14030}, mrnumber = {2266888}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2210/} }
TY - JOUR AU - Ishii, Shihoko TI - The Local Nash problem on arc families of singularities JO - Annales de l'Institut Fourier PY - 2006 SP - 1207 EP - 1223 VL - 56 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2210/ DO - 10.5802/aif.2210 LA - en ID - AIF_2006__56_4_1207_0 ER -
%0 Journal Article %A Ishii, Shihoko %T The Local Nash problem on arc families of singularities %J Annales de l'Institut Fourier %D 2006 %P 1207-1223 %V 56 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2210/ %R 10.5802/aif.2210 %G en %F AIF_2006__56_4_1207_0
Ishii, Shihoko. The Local Nash problem on arc families of singularities. Annales de l'Institut Fourier, Volume 56 (2006) no. 4, pp. 1207-1223. doi : 10.5802/aif.2210. http://archive.numdam.org/articles/10.5802/aif.2210/
[1] Diviseurs essentiels, composantes essentielle des variétés toriques singulières, Duke Math. J., Volume 91 (1998), pp. 609-620 | DOI | MR | Zbl
[2] Système générateur minimal, diviseurs essentiels et G-désingularisation, Tohoku Math. J., Volume 47 (1995), pp. 125-149 | DOI | MR | Zbl
[3] Introduction to toric varieties, Annals of Mathematics Studies, 131, Princeton University Press, Princeton, NJ, 1993 (The William H. Roever Lectures in Geometry) | MR | Zbl
[4] Embedded topological classification of quasi-ordinary singularities, Mem. Amer. Math. Soc., Volume 74 (1988) no. 388, pp. 109-129 (With an appendix by Joseph Lipman) | MR | Zbl
[5] Resolution of singularities of an algebraic variety over a field of characteristic zero: I, II, Annals of Math., Volume 79 (1964), pp. 109-326 | DOI | MR | Zbl
[6] The arc space of a toric variety, J. Algebra, Volume 278 (2004), pp. 666-683 | DOI | MR | Zbl
[7] Arcs, valuations and the Nash map, J. reine angew. Math, Volume 588 (2005), pp. 71-92 | DOI | MR | Zbl
[8] The Nash problem on arc families of singularities, Duke Math. J., Volume 120 (2003) no. 3, pp. 601-620 | DOI | MR | Zbl
[9] Arcs and wedges on sandwiched surface singularities, Amer. J. Math., Volume 121 (1999), pp. 1191-1213 | DOI | MR | Zbl
[10] Quasi-ordinary singularities of embedded surfaces, Harvard University (1965) (Ph. D. Thesis)
[11] Quasi-ordinary singularities of surfaces in , Singularities, Part 2 (Arcata, Calif., 1981) (Proc. Sympos. Pure Math.), Volume 40, Amer. Math. Soc., Providence, RI, 1983, pp. 161-172 | MR | Zbl
[12] Arc structure of singularities, Duke Math. J., Volume 81 (1995), pp. 31-38 | DOI | MR | Zbl
[13] Topological types of quasi-ordinary singularities, Proc. AMS, Volume 117 (1993), pp. 53-59 | DOI | MR | Zbl
[14] Toric embedded resolutions of quasi-ordinary hypersurface singularities, Ann. Inst. Fourier (Grenoble), Volume 53 (2003), pp. 1819-1881 | DOI | Numdam | MR | Zbl
[15] A class of non-rational surface singularities for which the Nash map is bijective (ath.AG/0410145)
[16] Image of Nash map in terms of wedges, C. R. Acad. Sci. Ser. I, Volume 338 (2004), pp. 385-390 | MR | Zbl
[17] Families of arcs on rational surface singularities, Manuscr. Math., Volume 88 (1995), pp. 321-333 | DOI | MR | Zbl
[18] Jets via Hasse-Schmidt derivations (preprint AG/0407113)
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