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.
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