no. 3
Real and complex analytic sets. The relevance of Segre varieties
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 447-454.

Let X⊂ℂ n n be a closed real-analytic subset and put

𝒜:={z∈X∣∃A⊂X,germofacomplex-analyticset,z∈A,dim z A>0}
This article deals with the question of the structure of 𝒜. In the main result a natural proof is given for the fact, that 𝒜 always is closed. As a main tool an interesting relation between complex analytic subsets of X of positive dimension and the Segre varieties of X is proved and exploited.

Classification : 32B10, 32C07 
@article{ASNSP_2008_5_7_3_447_0,
     author = {Diederich, Klas and Mazzilli, Emmanuel},
     title = {Real and complex analytic sets. {The} relevance of {Segre} varieties},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {447--454},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {3},
     year = {2008},
     mrnumber = {2466436},
     zbl = {1178.32006},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2008_5_7_3_447_0/}
}
TY  - JOUR
AU  - Diederich, Klas
AU  - Mazzilli, Emmanuel
TI  - Real and complex analytic sets. The relevance of Segre varieties
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2008
SP  - 447
EP  - 454
VL  - 7
IS  - 3
PB  - Scuola Normale Superiore, Pisa
UR  - http://www.numdam.org/item/ASNSP_2008_5_7_3_447_0/
LA  - en
ID  - ASNSP_2008_5_7_3_447_0
ER  - 
%0 Journal Article
%A Diederich, Klas
%A Mazzilli, Emmanuel
%T Real and complex analytic sets. The relevance of Segre varieties
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2008
%P 447-454
%V 7
%N 3
%I Scuola Normale Superiore, Pisa
%U http://www.numdam.org/item/ASNSP_2008_5_7_3_447_0/
%G en
%F ASNSP_2008_5_7_3_447_0
Diederich, Klas; Mazzilli, Emmanuel. Real and complex analytic sets. The relevance of Segre varieties. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 447-454. http://www.numdam.org/item/ASNSP_2008_5_7_3_447_0/

[1] E. Bishop, Condition for the analyticity of certain sets, Michigan Math. J. 11 (1964), 289-304. | MR | Zbl

[2] E. M. Chirka, “Complex Analytic Sets”, Kluwer, Dordrecht, 1990. | MR | Zbl

[3] J. D'Angelo Real hypersurfaces, orders of contact, and applications, Ann. of Math. 115 (1982), 615-637. | MR | Zbl

[4] J. P. D'Angelo, “Several Complex Variables and the Geometry of Real Hypersurfaces”, CRC Press, Boca Raton, FL, 1993. | MR | Zbl

[5] K. Diederich and J. E. Fornæss, Pseudoconvex domains with real analytic boundary, Ann. of Math. 107 (1978), 371-384. | MR | Zbl

[6] K. Diederich and S. Pinchuk, Uniform volume estimates for holomorphic families of analytic sets, Proc. Steklov Inst. Math., 235 (2001), 52-56. | MR | Zbl

[7] J. Kohn, Subellipticity of the ∂ ¯-Neumann problem on pseudoconvex domains: Sufficient conditions, Acta. Math. 142 (1979), 79-122. | MR | Zbl

[8] E. Mazzilli, Germes d'ensembles analytiques dans une hypersurface algébrique, Ark. Mat. 44 (2006), 327-333. | MR | Zbl