On semialgebraic tangent cones

• Autorzy: Fortuna, E. , Ferrarotti, M.
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the following question: which semialgebraic subsets of [R^n] can be realized as tangent cones to real algebraic subsets of [R^n]? At first we prove that the answer is positive for every closed semialgebraic cone in [R^n] of dimension [is less than or equal to 2]. Then, for closed semialgebraic cones A in [R^n] admitting a sufficiently nice algebraic presentation, we explicitely give equations of an algebraic subset V [...] [R^n] having A as its tangent come.

Słowa kluczowe

PL

geometria algebraiczna; real algebraic geometry \@eng\; styczne stożkowe

EN

algebraic geometry; real analytic geometry; semialgebraic sets; tangent cones

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no 4
• Strony: 383--390
• Opis fizyczny: Bibliogr. 4 poz.,

Twórcy

autor

Fortuna, E.

• Dipartamento di Matematica, Uniwersita di Pisa, Via Buonarotti 2, 56127 Pisa, Italy,

autor

Ferrarotti, M.

• Dipartamento di Matematica, Uniwersita di Pisa, Via Buonarotti 2, 56127 Pisa, Italy,

Bibliografia

• [1] Н. Whitney, Tangents to on analytic variety, Ann. of Math., 81 (1965) 496-549.
• [2] D. Cox, J. Little, D. O'Shea, Ideals, varieties and algorithms, Springer-Verlag, 1992.
• [3] D. O' Shea, L. Wilson, Tangent end normnal cones to real surfaces, Chinese Quarterly J. of Math., 10 (1995) 62-71.
• [4] J. М. Ruiz, A note on а separation problem, Arch. Math., 43 (1984) 422-426.