A note on global Nash subvarieties and Artin-Mazur theorem
Tancredi, Alessandro ; Tognoli, Alberto
Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 425-431 / Harvested from Biblioteca Digitale Italiana di Matematica
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It is shown that every connected global Nash subvariety of Rn 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.

Si prova che ogni sottospazio di Nash connesso di Rn che abbia equazioni globali è Nash isomorfo ad una componente connessa di una varietà algebrica che, nel caso compatto, può essere scelta con due sole componenti connesse arbitrariamente vicine. Alcuni esempi illustrano i limiti dei risultati ottenuti e degli strumenti utilizzati.

Publié le : 2004-06-01
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     author = {Alessandro Tancredi and Alberto Tognoli},
     title = {A note on global Nash subvarieties and Artin-Mazur theorem},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {425-431},
     zbl = {1150.14015},
     mrnumber = {2072945},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_425_0}
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Tancredi, Alessandro; Tognoli, Alberto. A note on global Nash subvarieties and Artin-Mazur theorem. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 425-431. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_425_0/

[AK] Akbulut, S.-King, H., Topology of real algebraic sets, Maht. Sci. Research Institute Publ.25, Springer, Berlin (1992). | MR 1225577 | Zbl 0808.14045

[BCR] Bochnack, J.-Coste, M.-Roy, M. F., Real algebraic geometry, Springer, Berlin, 1998. | MR 1659509 | Zbl 0912.14023

[CRS] Coste, M.-Ruiz, R.-Shiota, M., Approximation in Nash manifolds, Amer. J. Math., 117 (1995), 905-927. | MR 1342835 | Zbl 0873.32007

[CS] Coste, M.-Shiota, M., Nash functions on noncompact Nash manifolds, Ann. Scient. Éc. Norm. Sup., 33 (2000), 139-149. | MR 1743722 | Zbl 0981.14027

[EV] Encinas, S.-Villamayor, O., A new theorem of desingularization over fields of characteristic zero, Preprint arXiv:math.AG/0101208

[NT] 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. | MR 1413268 | Zbl 0879.32013

[TT1] Tancredi, A.-Tognoli, A., On the extension of Nash functions, Math. Ann.288 (1990), 595-604. | MR 1081265 | Zbl 0699.32006

[TT2] Tancredi, A.-Tognoli, A., Some remarks on the classification of complex Nash vector bundles, Bull. Sci. math., 17 (1993), 177-183. | MR 1216006 | Zbl 0798.32010

[TT3] Tancredi, A.-Tognoli, A., On the algebraic approximation of Nash maps, Ann. Univ. Ferrara, 38 (1992), 107-115. | MR 1261965 | Zbl 0858.14028

[To] Tognoli, A., Algebraic approximation of manifolds and spaces, Sém. Bourbaki, 548 (1979/80). | Zbl 0456.57012

[Wa] Wallace, A. H., Algebraic approximation of manifolds, Proc. London Math. Soc. (3), 7 (1957), 196-210. | MR 87205 | Zbl 0081.37802