## Linearly normal curves in $${\mathbb P}^4$$ and $${\mathbb P}^5$$.(English)Zbl 1033.14021

Summary: We extend a theorem proved by A. Dolcetti and G. Pareschi [Math. Z. 198, No. 1, 73–82 (1988; Zbl 0619.14003)], concerning the existence of linearly normal curves in $${\mathbb P}^3$$, to similar ones for $${\mathbb P}^4$$ and $${\mathbb P}^5$$. However the result seems to be false for $${\mathbb P}^n$$, $$n\geq 6$$.

### MSC:

 14H50 Plane and space curves 14H25 Arithmetic ground fields for curves

### Keywords:

linearly normal curve

Zbl 0619.14003