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Some properties of global semianalytic subsets of coherent surfaces


Andradas Heranz, Carlos and Díaz-Cano Ocaña, Antonio (2004) Some properties of global semianalytic subsets of coherent surfaces. Illinois Journal of Mathematics, 48 (2). pp. 519-537. ISSN 0019-2082

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Let X subset of R-n be a coherent analytic surface. We show that the connected components of global analytic subsets of X are global and we compute the stability index and Brocker's t-invariant of X. We also state a real Nullstellensatz for normal surfaces.

Item Type:Article
Uncontrolled Keywords:Coherent surfaces, real analytic sets, analytic functions.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14762

F. Acquistapace, F. Broglia, and M. Shiota, The niteness property and H�ormander- lojasiewicz inequality in global semianalytic sets, preprint available at

C. Andradas and E. Becker, A note on the real spectrum of analytic functions on an analytic manifold of dimension one, Real analytic and algebraic geometry (Trento, 1988), Lecture Notes in Math., vol. 1420, Springer, Berlin, 1990, pp. 1{21.

C. Andradas, L. Br�ocker, and J. M. Ruiz, Constructible sets in real geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 33, Springer- Verlag, Berlin, 1996. C. Andradas and A. Daz-Cano, Closed stability index of excellent henselian local rings, Math. Z., to appear.

C. Andradas, A. Daz-Cano, and J. M. Ruiz, The Artin-Lang property for normal real analytic surfaces, J. Reine Angew. Math. 556 (2003), 99{111.

E. Becker, On the real spectrum of a ring and its application to semialgebraic geometry, Bull. Amer. Math. Soc. (N.S.) 15 (1986), 19{60.

J. Bochnak, M. Coste, and M.-F. Roy, Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 36, Springer-Verlag, Berlin, 1998.

J. Bochnak and J.-J. Risler, Le theoreme des zeros pour les varietes analytiques reelles de dimension 2, Ann. Sci. Ecole Norm. Sup. (4) 8 (1975), 353{363.

L. Br�ocker, On basic semialgebraic sets, Exposition. Math. 9 (1991), 289{334.

F. Broglia and F. Pieroni, Separation of global semianalytic subsets of 2-dimensional analytic manifolds, Pacic J. Math. 214 (2004), 1{16.

F. Bruhat and H. Whitney, Quelques proprietes fondamentales des ensembles analytiques-reels, Comment. Math. Helv. 33 (1959), 132{160.

A. Castilla, Artin-Lang property for analytic manifolds of dimension two, Math. Z. 217 (1994), 5{14.

A. Castilla and C. Andradas, Connected components of global semianalytic subsets of 2-dimensional analytic manifolds, J. Reine Angew. Math. 475 (1996), 137{148.

A. Daz-Cano, The t-invariant of analytic set germs of dimension 2, J. Pure Appl. Algebra 160 (2001), 157{168.

A. Daz-Cano and C. Andradas, Complexity of global semianalytic sets in a real analytic manifold of dimension 2, J. Reine Angew. Math. 534 (2001), 195{208.

M. Galbiati, Sur l'image d'un morphisme analytique reel propre, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), 311{319.

P. Jaworski, The 17th Hilbert problem for noncompact real analytic manifolds, Real algebraic geometry (Rennes, 1991), Lecture Notes in Math., vol. 1524, Springer, Berlin, 1992, pp. 289{295.

T. Y. Lam, An introduction to real algebra, Rocky Mountain J. Math. 14 (1984), 767{814.

M. A. Marshall, Spaces of orderings and abstract real spectra, Lecture Notes in Mathematics, vol. 1636, Springer-Verlag, Berlin, 1996.

J. M. Ruiz, On Hilbert's 17th problem and real Nullstellensatz for global analytic functions, Math. Z. 190 (1985), 447{454.

Deposited On:17 Apr 2012 11:46
Last Modified:06 Feb 2014 10:08

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