The Local Nash problem on arc families of singularities

Shihoko Ishii[1]

  • [1] Tokyo Institute of Technology Department of Mathematics Oh-Okayama, Meguro 152-8551 Tokyo (Japan)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 4, page 1207-1223
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Ishii, Shihoko. "The Local Nash problem on arc families of singularities." Annales de l’institut Fourier 56.4 (2006): 1207-1223. <http://eudml.org/doc/10170>.

@article{Ishii2006,
abstract = {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.},
affiliation = {Tokyo Institute of Technology Department of Mathematics Oh-Okayama, Meguro 152-8551 Tokyo (Japan)},
author = {Ishii, Shihoko},
journal = {Annales de l’institut Fourier},
keywords = {Arc space; Nash problem; singularities; arc space},
language = {eng},
number = {4},
pages = {1207-1223},
publisher = {Association des Annales de l’institut Fourier},
title = {The Local Nash problem on arc families of singularities},
url = {http://eudml.org/doc/10170},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Ishii, Shihoko
TI - The Local Nash problem on arc families of singularities
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 4
SP - 1207
EP - 1223
AB - 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.
LA - eng
KW - Arc space; Nash problem; singularities; arc space
UR - http://eudml.org/doc/10170
ER -

References

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  10. J. Lipman, Quasi-ordinary singularities of embedded surfaces, (1965) 
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  12. J. F. Nash, Arc structure of singularities, Duke Math. J. 81 (1995), 31-38 Zbl0880.14010MR1381967
  13. K. Oh, Topological types of quasi-ordinary singularities, Proc. AMS 117 (1993), 53-59 Zbl0791.32018MR1106181
  14. P. D. Gonález Pérez, Toric embedded resolutions of quasi-ordinary hypersurface singularities, Ann. Inst. Fourier (Grenoble) 53 (2003), 1819-1881 Zbl1052.32024MR2038781
  15. C. Plenat, P. Popescu-Pampu, A class of non-rational surface singularities for which the Nash map is bijective Zbl1119.14007
  16. A. J. Reguera, Image of Nash map in terms of wedges, C. R. Acad. Sci. Ser. I 338 (2004), 385-390 Zbl1044.14032MR2057169
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  18. P. Vojta, Jets via Hasse-Schmidt derivations Zbl1194.13027

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