no. 12
Analytic Geometry
Approximation of analytic sets with proper projection by Nash sets
[Approximation des ensembles analytiques à projection propre par des ensembles de Nash]

Présenté par : Jean-Pierre Demailly

Bilski, Marcin1
1 Computer Science Department, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland
Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 747-750.

Soit X⊂U×Ck un ensemble analytique de dimension pure tel que la projection π:X→U est surjective et propre, où U est un domaine de Runge. Nous démontrons que X est approchable par des ensembles de Nash.

Let X be an analytic subset of U×Ck of pure dimension such that the projection π:X→U is surjective and proper, where U is a Runge domain. We show that X can be approximated by Nash sets.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.016
Bilski, Marcin 1

1 Computer Science Department, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland 
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Bilski, Marcin. Approximation of analytic sets with proper projection by Nash sets. Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 747-750. doi : 10.1016/j.crma.2005.10.016. http://archive.numdam.org/articles/10.1016/j.crma.2005.10.016/

[1] Barlet, D. Espace analytique réduit des cycles analytiques complexes compacts d'un espace analytique complexe de dimension finie, Fonctions de plusieurs variables complexes, II, Sém. François Norguet, 1974–1975, Lecture Notes in Math., vol. 482, Springer, Berlin, 1975, pp. 1-158

[2] Bilski, M. On approximation of analytic sets, Manuscripta Math., Volume 114 (2004), pp. 45-60

[3] Chirka, E.M. Complex Analytic Sets, Kluwer Academic Publishers, Dordrecht, 1989

[4] Demailly, J.-P. Monge–Ampere operators, Lelong numbers and intersection theory, Complex Analysis and Geometry, Univ. Ser. Math., Plenum, New York, 1993, pp. 115-193

[5] Demailly, J.-P.; Lempert, L.; Shiffman, B. Algebraic approximation of holomorphic maps from Stein domains to projective manifolds, Duke Math. J., Volume 76 (1994), pp. 333-363

[6] Lelong, P. Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France, Volume 85 (1957), pp. 239-262

[7] Lempert, L. Algebraic approximations in analytic geometry, Invent. Math., Volume 121 (1995), pp. 335-354

[8] Tancredi, A.; Tognoli, A. Relative approximation theorems of Stein manifolds by Nash manifolds, Boll. Un. Mat. Ital. A, Volume 3 (1989), pp. 343-350

[9] Tancredi, A.; Tognoli, A. On the extension of Nash functions, Math. Ann., Volume 288 (1990), pp. 595-604

[10] Tancredi, A.; Tognoli, A. On the relative Nash approximation of analytic maps, Rev. Mat. Complut., Volume 11 (1998), pp. 185-201

[11] Tworzewski, P. Intersections of analytic sets with linear subspaces, Ann. Sc. Norm. Sup. Pisa, Volume 17 (1990), pp. 227-271

[12] Tworzewski, P. Intersection theory in complex analytic geometry, Ann. Polon. Math., Volume 62 (1995) no. 2, pp. 177-191

[13] Tworzewski, P.; Winiarski, T. Continuity of intersection of analytic sets, Ann. Polon. Math., Volume 42 (1983), pp. 387-393

[14] Whitney, H. Complex Analytic Varieties, Addison-Wesley Publishing Co., Reading, MA, 1972

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