Local approximation of semialgebraic sets

Ferrarotti, Massimo; Fortuna, Elisabetta; Wilson, Les

Ferrarotti, Massimo ; Fortuna, Elisabetta ; Wilson, Les

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 1-11.

Résumé

Let $A$ be a closed semialgebraic subset of euclidean space of codimension at least one, and containing the origin $O$ as a non-isolated point. We prove that, for every real $s \geq 1$ , there exists an algebraic set $V$ which approximates $A$ to order $s$ at $O$ . The special case $s = 1$ generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.

MR Zbl

Classification : 14P10

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     title = {Local approximation of semialgebraic sets},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {1--11},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
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     mrnumber = {1994799},
     zbl = {1051.14065},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_1_1_0/}
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Ferrarotti, Massimo; Fortuna, Elisabetta; Wilson, Les. Local approximation of semialgebraic sets. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 1-11. http://www.numdam.org/item/ASNSP_2002_5_1_1_1_0/

Bibliographie
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