The genus of curves in \({\mathbb{P}}^ 4\) and \({\mathbb{P}}^ 5\) (Q923640)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The genus of curves in \({\mathbb{P}}^ 4\) and \({\mathbb{P}}^ 5\) |
scientific article; zbMATH DE number 4171093
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The genus of curves in \({\mathbb{P}}^ 4\) and \({\mathbb{P}}^ 5\) |
scientific article; zbMATH DE number 4171093 |
Statements
The genus of curves in \({\mathbb{P}}^ 4\) and \({\mathbb{P}}^ 5\) (English)
0 references
1989
0 references
The aim of this paper is to establish the range \((d,g)\) \(d=\) the degree, \(g=\) the genus for smooth nondegenerate curves in \({\mathbb{P}}^ 4\) and \({\mathbb{P}}^ 5\). As well known, for curves in \({\mathbb{P}}^ 3\) the range was established by Halphen and Gruson-Peskine. The author uses the method of Gruson and Peskine, by constructing the searched curves on Del Pezzo or Bordiga surfaces. For an independent work on the same subject, see also \textit{O. Păsărescu}, Arch. Math. 51, No.3, 255-265 (1988; Zbl 0632.14029).
0 references
Del Pezzo surface
0 references
degree
0 references
genus
0 references
Bordiga surfaces
0 references
0.95209014
0 references
0.93544173
0 references
0.91979575
0 references
0.90946704
0 references
0.88780016
0 references
