On projective manifolds admitting 3-gonal or 4-gonal curve sections
Let <em>X</em> be a projective manifold, of dimension <em>n≥3</em>, and <em>L</em> a very ample line bundle on <em>X</em>. In this paper we investigate the pairs <em>(X,L)</em> with the following property: there exists a transversal interse...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Università degli Studi di Catania
1989-10-01
|
| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/680 |
| Summary: | Let <em>X</em> be a projective manifold, of dimension <em>n≥3</em>, and <em>L</em> a very ample line bundle on <em>X</em>. In this paper we investigate the pairs <em>(X,L)</em> with the following property: there exists a transversal intersection of <em>n-1</em> members of <em>|L|</em> which is a smooth <em>d</em>-gonal curve (<em>d=3,4</em>). We prove, under suitable assumptions, that <em>n≤4</em> or <em>5</em> (resp. if <em>d=3</em> or <em>4</em>) and <em>(X,L)</em> is a fibration over <strong>P</strong><sup>1 </sup>with genera; fibre a rational cubic (resp. quartic) scroll. |
|---|---|
| ISSN: | 0373-3505 2037-5298 |