Osculating subspaces, normal rational curves and generalized strange curves

摘要

Let C is contained in P~n be an integral non-degenerate projective curve. Fix an integer t with 1 ≤ t ≤ n - 1. In this paper, we study properties of the family of all oseulating t-subspaces at general points of C. We work over an algebraically closed field K and set p := char (K) ≥ 0. We are mainly interested in the case in which K is the algebraic closure of a finite field GF(q), because in this case, some concepts may be translated in the set up of finite geometries (see the use of [4] in Section 3).