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On semialgebraic tangent cones

Fortuna E.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 4

383-390

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.