A note on global Nash subvarieties and Artin-Mazur theorem

Alessandro Tancredi; Alberto Tognoli

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 2, page 425-431
  • ISSN: 0392-4041

Abstract

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It is shown that every connected global Nash subvariety of R n is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.

How to cite

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Tancredi, Alessandro, and Tognoli, Alberto. "A note on global Nash subvarieties and Artin-Mazur theorem." Bollettino dell'Unione Matematica Italiana 7-B.2 (2004): 425-431. <http://eudml.org/doc/195834>.

@article{Tancredi2004,
abstract = {It is shown that every connected global Nash subvariety of $\mathbb\{R\}^\{n\}$ is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.},
author = {Tancredi, Alessandro, Tognoli, Alberto},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {425-431},
publisher = {Unione Matematica Italiana},
title = {A note on global Nash subvarieties and Artin-Mazur theorem},
url = {http://eudml.org/doc/195834},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Tancredi, Alessandro
AU - Tognoli, Alberto
TI - A note on global Nash subvarieties and Artin-Mazur theorem
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/6//
PB - Unione Matematica Italiana
VL - 7-B
IS - 2
SP - 425
EP - 431
AB - It is shown that every connected global Nash subvariety of $\mathbb{R}^{n}$ is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.
LA - eng
UR - http://eudml.org/doc/195834
ER -

References

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  1. AKBULUT, S.- KING, H., Topology of real algebraic sets, Maht. Sci. Research Institute Publ.25, Springer, Berlin (1992). Zbl0808.14045MR1225577
  2. BOCHNACK, J.- COSTE, M.- ROY, M. F., Real algebraic geometry, Springer, Berlin, 1998. Zbl0912.14023MR1659509
  3. COSTE, M.- RUIZ, R.- SHIOTA, M., Approximation in Nash manifolds, Amer. J. Math., 117 (1995), 905-927. Zbl0873.32007MR1342835
  4. COSTE, M.- SHIOTA, M., Nash functions on noncompact Nash manifolds, Ann. Scient. Éc. Norm. Sup., 33 (2000), 139-149. Zbl0981.14027MR1743722
  5. ENCINAS, S.- VILLAMAYOR, O., A new theorem of desingularization over fields of characteristic zero, Preprint arXiv:math.AG/0101208 
  6. NARDELLI, G.- TANCREDI, A., A note on the extension of analytic functions off real analytic subsets, Revista Matemática de la Universidad Complutense de Madrid, 9 (1996), 85-99. Zbl0879.32013MR1413268
  7. TANCREDI, A.- TOGNOLI, A., On the extension of Nash functions, Math. Ann.288 (1990), 595-604. Zbl0699.32006MR1081265
  8. TANCREDI, A.- TOGNOLI, A., Some remarks on the classification of complex Nash vector bundles, Bull. Sci. math., 17 (1993), 177-183. Zbl0798.32010MR1216006
  9. TANCREDI, A.- TOGNOLI, A., On the algebraic approximation of Nash maps, Ann. Univ. Ferrara, 38 (1992), 107-115. Zbl0858.14028MR1261965
  10. TOGNOLI, A., Algebraic approximation of manifolds and spaces, Sém. Bourbaki, 548 (1979/80). Zbl0456.57012
  11. WALLACE, A. H., Algebraic approximation of manifolds, Proc. London Math. Soc. (3), 7 (1957), 196-210. Zbl0081.37802MR87205

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