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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the products of Nash subvarieties by spheres


Authors: Alessandro Tancredi and Alberto Tognoli
Journal: Proc. Amer. Math. Soc. 134 (2006), 983-987
MSC (2000): Primary 14P05; Secondary 14P20, 58A07
Published electronically: September 28, 2005
MathSciNet review: 2196028
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Abstract: We show that the product of any sphere by any compact connected component of a real algebraic variety is Nash isomorphic to a real algebraic variety, and we deduce such a result for some non-compact components, too. It follows also that the product of any sphere by any compact global Nash subvariety of $ \mathbb{R}^n$ is Nash isomorphic to a real algebraic variety.


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Additional Information

Alessandro Tancredi
Affiliation: Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli, 1, 06123 Perugia (PG), Italy
Email: altan@unipg.it

Alberto Tognoli
Affiliation: Dipartimento di Matematica, Università di Trento, Via Sommarive, 58, 38050 Povo (TN), Italy
Email: tognoli@science.unitn.it

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08246-8
PII: S 0002-9939(05)08246-8
Keywords: Nash function, global Nash subvariety
Received by editor(s): February 9, 2004
Received by editor(s) in revised form: November 4, 2004
Published electronically: September 28, 2005
Additional Notes: The authors are members of GNSAGA of INDAM. This work was partially supported by MIUR and by European Contract HPRN-CT-2001-00271.
Communicated by: Michael Stillman
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.