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

Păsărescu, Ovidiu

An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 9, No. 1, 73-80 (2001).

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

Citations:

Zbl 0619.14003