On projective manifolds admitting 3-gonal or 4-gonal curve sections
Abstract
Let X be a projective manifold, of dimension n≥3, and L a very ample line bundle on X. In this paper we investigate the pairs (X,L) with the following property: there exists a transversal intersection of n-1 members of |L| which is a smooth d-gonal curve (d=3,4). We prove, under suitable assumptions, that n≤4 or 5 (resp. if d=3 or 4) and (X,L) is a fibration over P1 with genera; fibre a rational cubic (resp. quartic) scroll.The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
