Equivalence of the Nash conjecture for primitive and sandwiched singularities

Author:
Jesús Fernández-Sánchez

Journal:
Proc. Amer. Math. Soc. **133** (2005), 677-679

MSC (2000):
Primary 14B05, 14E15, 32B10

Published electronically:
August 4, 2004

MathSciNet review:
2113914

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that in order to prove the Nash Conjecture for sandwiched singularities it is enough to prove it for primitive singularities.

**[1]**Eduardo Casas-Alvero,*Singularities of plane curves*, London Mathematical Society Lecture Note Series, vol. 276, Cambridge University Press, Cambridge, 2000. MR**1782072****[2]**Jesús Fernández-Sánchez,*On sandwiched singularities and complete ideals*, J. Pure Appl. Algebra**185**(2003), no. 1-3, 165–175. MR**2006424**, 10.1016/S0022-4049(03)00082-3**[3]**J. FERNÁNDEZ-SÁNCHEZ, Nash families of smooth arcs on a sandwiched singularity. To appear in*Math. Proc. Cambridge. Philos. Soc.***[4]**Shihoko Ishii and János Kollár,*The Nash problem on arc families of singularities*, Duke Math. J.**120**(2003), no. 3, 601–620. MR**2030097**, 10.1215/S0012-7094-03-12034-7**[5]**John F. Nash Jr.,*Arc structure of singularities*, Duke Math. J.**81**(1995), no. 1, 31–38 (1996). A celebration of John F. Nash, Jr. MR**1381967**, 10.1215/S0012-7094-95-08103-4**[6]**C. PLÉNAT, A propos de la conjecture de Nash.*Preprint.*math.AG/0301358.**[7]**Mark Spivakovsky,*Sandwiched singularities and desingularization of surfaces by normalized Nash transformations*, Ann. of Math. (2)**131**(1990), no. 3, 411–491. MR**1053487**, 10.2307/1971467

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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:
http://dx.doi.org/10.1090/S0002-9939-04-07643-9

Keywords:
Sandwiched singularity,
arc,
infinitely near point

Received by editor(s):
August 27, 2003

Received by editor(s) in revised form:
November 1, 2003

Published electronically:
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

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.