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Equivalence of the Nash conjecture for primitive and sandwiched singularities
Author(s):
Jesús
Fernández-Sánchez
Journal:
Proc. Amer. Math. Soc.
133
(2005),
677-679.
MSC (2000):
Primary 14B05, 14E15, 32B10
Posted:
August 4, 2004
MathSciNet review:
2113914
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Abstract:
We show that in order to prove the Nash Conjecture for sandwiched singularities it is enough to prove it for primitive singularities.
References:
-
- [1]
- E. CASAS-ALVERO, Singularities of plane curves, volume 276 of London Math. Soc. Lecture Note Series. Cambridge University Press, 2000. MR 1782072 (2003b:14035)
- [2]
- J. FERNÁNDEZ-SÁNCHEZ, On sandwiched singularities and complete ideals. J. Pure Appl. Algebra, 185: 165-175, 2003. MR 2006424
- [3]
- J. FERNÁNDEZ-SÁNCHEZ, Nash families of smooth arcs on a sandwiched singularity. To appear in Math. Proc. Cambridge. Philos. Soc.
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- S. ISHII, J. KOLLÁR, The Nash problem on arc families of singularities. Preprint. math.AG/0207171. Duke Math. J., 120: 601-620, 2003. MR 2030097
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- J. NASH, Arc structure of singularities. Duke Math. J., 81:31-38, 1996. MR 1381967 (98f:14011)
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- [7]
- M. SPIVAKOVSKY, Sandwiched singularities and desingularization of surfaces by normalized transformations. Ann. of Math., 131:411-491, 1990. MR 1053487 (91e:14013)
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Additional Information:
Jesús
Fernández-Sánchez
Affiliation:
Departament d'Àlgebra i Geometria, Universitat de Barcelona, Gran Via, 585, E--08007, Barcelona, Spain
Email:
jsan@cerber.mat.ub.es
DOI:
10.1090/S0002-9939-04-07643-9
PII:
S 0002-9939(04)07643-9
Keywords:
Sandwiched singularity,
arc,
infinitely near point
Received by editor(s):
August 27, 2003
Received by editor(s) in revised form:
November 1, 2003
Posted:
August 4, 2004
Additional Notes:
The author was partially supported by Generalitat de Catalunya 2001SGR00071 and EAGER, European Union contract HPRN-CT-2000-00099
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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