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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

Citations:

Zbl 0619.14003
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