Let X be a projective manifold, of dimension n > 2, and L a very ample line bundle on X. In this paper we investigate the paits (X,L) with the following property: there exists a transversal intersection of n-1 members of |L| whihc is a smooth d-gonal curve (d = 3,4). We prove , under suitable assumptions, that n <5 or 6 (resp. if d = 3 or d = 4) and (X,L) is a fibration over P^1 with general fibre a rational cubic (resp. quartic) scroll.

Brivio, S. (1989). On projective manifolds adfmitting 3-gonal or 4-gonal curve sections. LE MATEMATICHE, XLIV(II), 163-172.

On projective manifolds adfmitting 3-gonal or 4-gonal curve sections

S. Brivio
1989

Abstract

Let X be a projective manifold, of dimension n > 2, and L a very ample line bundle on X. In this paper we investigate the paits (X,L) with the following property: there exists a transversal intersection of n-1 members of |L| whihc is a smooth d-gonal curve (d = 3,4). We prove , under suitable assumptions, that n <5 or 6 (resp. if d = 3 or d = 4) and (X,L) is a fibration over P^1 with general fibre a rational cubic (resp. quartic) scroll.
Articolo in rivista - Articolo scientifico
Projective manifolds. Trigonal curve sections.
English
1989
XLIV
II
163
172
none
Brivio, S. (1989). On projective manifolds adfmitting 3-gonal or 4-gonal curve sections. LE MATEMATICHE, XLIV(II), 163-172.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/254358
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