Real and complex analytic sets. The relevance of Segre varieties
Klas Diederich; Emmanuel Mazzilli
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)
- Volume: 7, Issue: 3, page 447-454
- ISSN: 0391-173X
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topDiederich, Klas, and Mazzilli, Emmanuel. "Real and complex analytic sets. The relevance of Segre varieties." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.3 (2008): 447-454. <http://eudml.org/doc/272268>.
@article{Diederich2008,
abstract = {Let $X\subset \{\mathbb \{C\}^\{n\}\}^n$ be a closed real-analytic subset and put\[ \mathcal \{A\}:=\lbrace z\in X\mid \exists \ A\subset X,\text\{ germ of a complex-analytic set, \} z\in A,\, \dim \_\{z\} A>0 \rbrace \]This article deals with the question of the structure of $\mathcal \{A\}$. In the main result a natural proof is given for the fact, that $\mathcal \{A\}$ 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.},
author = {Diederich, Klas, Mazzilli, Emmanuel},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {real-analytic sets; complex-analytic subsets; Segre varieties},
language = {eng},
number = {3},
pages = {447-454},
publisher = {Scuola Normale Superiore, Pisa},
title = {Real and complex analytic sets. The relevance of Segre varieties},
url = {http://eudml.org/doc/272268},
volume = {7},
year = {2008},
}
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
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 3
SP - 447
EP - 454
AB - Let $X\subset {\mathbb {C}^{n}}^n$ be a closed real-analytic subset and put\[ \mathcal {A}:=\lbrace z\in X\mid \exists \ A\subset X,\text{ germ of a complex-analytic set, } z\in A,\, \dim _{z} A>0 \rbrace \]This article deals with the question of the structure of $\mathcal {A}$. In the main result a natural proof is given for the fact, that $\mathcal {A}$ 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.
LA - eng
KW - real-analytic sets; complex-analytic subsets; Segre varieties
UR - http://eudml.org/doc/272268
ER -
References
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