Real and complex analytic sets. The relevance of Segre varieties

Diederich, Klas; Mazzilli, Emmanuel

Diederich, Klas ; Mazzilli, Emmanuel

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 447-454.

Résumé

Let $X \subset {ℂ^{n}}^{n}$ be a closed real-analytic subset and put

𝒜 : = {z \in X ∣ \exists A \subset X, germ of a complex-analytic set, z \in 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.

MR 2466436 | Zbl 1178.32006

Classification : 32B10, 32C07

BibTeX
RIS

@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},
     zbl = {1178.32006},
     mrnumber = {2466436},
     language = {en},
     url = {http://archive.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
DA  - 2008///
SP  - 447
EP  - 454
VL  - Ser. 5, 7
IS  - 3
PB  - Scuola Normale Superiore, Pisa
UR  - http://archive.numdam.org/item/ASNSP_2008_5_7_3_447_0/
UR  - https://zbmath.org/?q=an%3A1178.32006
UR  - https://www.ams.org/mathscinet-getitem?mr=2466436
LA  - en
ID  - ASNSP_2008_5_7_3_447_0
ER  -

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://archive.numdam.org/item/ASNSP_2008_5_7_3_447_0/

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Cité par

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