Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 349p-362p
We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in , and extended to P^4 and P^5 in . In both these papers is used the idea appearing in  and consisting in adding hyperplane sections to the curves constructed in  (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply the same idea to the curves lying on some rational surfaces from P^n, constructed in [12, 3, 2] (see [13, 14] also).