Local approximation of semialgebraic sets
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, p. 1-11
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 s1, 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.
Classification:  14P10
@article{ASNSP_2002_5_1_1_1_0,
     author = {Ferrarotti, Massimo and Fortuna, Elisabetta and Wilson, Les},
     title = {Local approximation of semialgebraic sets},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     year = {2002},
     pages = {1-11},
     zbl = {1051.14065},
     mrnumber = {1994799},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_1_1_0}
}
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/

[B-C-R] J. Bochnak - M. Coste - M. F. Roy, “Géométrie algébrique réelle”, Springer-Verlag, 1987. | MR 949442 | Zbl 0633.14016

[B1] L. Bröcker, Families of semialgebraic sets and limits, In: “Real Algebraic Geometry” (Rennes 1991), M. Coste - L. Mahé - M.-F. Roy (eds.), Lecture Notes in Math., 1524, Springer-Verlag, Berlin, 1992, pp. 145-162. | MR 1226248 | Zbl 0849.14022

[B2] L. Bröcker, On the reduction of semialgebraic sets by real valuations, in: “Recent advances in real algebraic geometry and quadratic forms”, Contemp. Math., 155, Amer. Math. Soc., Providence, RI, 1994, pp. 75-95. | MR 1260702 | Zbl 0826.14038

[F-F-W] M. Ferrarotti - E. Fortuna - L. Wilson, Real algebraic varieties with prescribed tangent cones, Pacific J. Math. 194 (2000), 315-323. | MR 1760783 | Zbl 1036.14027

[K-R] K. Kurdyka - G. Raby, Densité des ensembles sous-analytiques, Ann. Inst. Fourier (Grenoble) 39 (1989), 753-771. | Numdam | MR 1030848 | Zbl 0673.32015