Some remarks on the semi-local extension of Nash maps

Springer Science and Business Media LLC - Tập 43 - Trang 51-63 - 1997
Alessandro Tancredi1
1Dipartimento di Matematica, Università di Perugia, Perugia, Italy

Tóm tắt

The paper deals with the extension of Nash maps off Nash subvarieties on a neighborhood of a compact set.

Tài liệu tham khảo

[BCR]J. Bochnak—M. Coste—M. F. Roy,Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge, Band 12, Springer, Berlin, Heidelberg, New York (1987). [CRS]M. Coste—J. M. Ruiz—M. Shiota,Approximation in compact Nash manifolds, Amer. J. Math.,117 (1995), pp. 905–927. [CS]M. Coste—M. Shiota,Nash Functions on noncompact Nash manifolds, Preprint, 1997. [DLS]J. P. Demailly—L. Lempert—B. Shiffman,Algebraic approximation of holomorphic maps from stein domains to projective manifolds, Duke Math. J.,76 (1994), pp. 333–363. [GT]S. Greco—C. Traverso,On seminormal schemes, Comp. Math.,40 (1980), pp. 325–365. [Le]L. Lempert,Algebraic approximation in analytic geometry, Inv. Math.,121 (1995), pp. 335–353. [Ma]H. Matzumura,Commutative algebra, Math. Lecture Note Series, vol.56, Benjamin, Reading, MA (1980). [Na]R. Narashiman,Introduction to the theory of analytic spaces, Lecture Notes in Mathematics,25, Springer, Berlin, Heidelberg, New York (1966). [NT]G. Nardelli—A. Tancredi,A note on the extension of analytic functions off real analytic subsets, Revista Matemática de la Universidad Complutense de Madrid,9 (1996), pp. 85–97. [Po]D. Popescu,General Néron desingularization, Nagoya Math. J.,100 (1985), pp. 97–126. [Qu]R. Quarez,Quelques problèmes ouverts sur les functions de Nash, Thèse, Rennes (1996). [Ru]M. J. Ruiz,The basic theory of power series, Advanced Lectures in Mathematics, Vieweg, Wiesbaden (1993). [Se]J. P. Serre,Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier,6 (1956), pp. 1–42. [Sh]M. Shiota,Nash manifolds, Lecture Notes in Math. 1269, Springer, Berlin, Heidelberg, New York (1987). [Sp]M. Spivakovsky,Smoothing of ring homomorphisms, approximation theorems and the Bass-Quillen conjecture, Preprint (1994). [Ta]A. Tancredi,Sulla complessificazione degli spazi di Nash, Ann. Univ. Ferrara,34 (1988), pp. 135–145. [TT1]A. Tancredi—A. Tognoli,On the extension of Nash functions, Math. Ann.,288 (1990), pp. 595–604. [TT2]A. Tancredi—A. Tognoli,Some remarks on the classification of complex Nash vector bundles, Bull. Sc. Math.,117 (1993), pp. 173–183. [TT3]A. Tancredi—A. Tognoli,On the relative Nash approximation of analytic maps, Revista Matemática de la Universidad Complutense de Madrid,11 (1998). [Za]W. R. Zame,Holomorphic convexity of compact sets in analytic spaces and the structure of algebras of holomorphic germs, Trans. Amer. Math. Soc.,222 (1976), pp. 107–127.