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 
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     title = {Real and complex analytic sets. {The} relevance of {Segre} varieties},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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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/

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