Let C be a smooth curve with a gn1, i.e. a linear system of dimension 1 and degree n, lying on a smooth projective surface S. Let φ:S → PN be the map associated to the line bundle KS+[C] and let D be a general divisor of the given linear system gn1. Let V be the linear space spanned by the image of D through φ. We study the case in which n′:=dim V=1 and in general we discuss the case in which n′ is small. The starting point is an analysis of the adjunction map φ using Bogomolov-Reider-Serrano techniques; several results from curve theory are also needed. © 1994 Kluwer Academic Publishers.
Curves and 0-cycles on projective surfaces
Andreatta, Marco;Ballico, Edoardo
1994-01-01
Abstract
Let C be a smooth curve with a gn1, i.e. a linear system of dimension 1 and degree n, lying on a smooth projective surface S. Let φ:S → PN be the map associated to the line bundle KS+[C] and let D be a general divisor of the given linear system gn1. Let V be the linear space spanned by the image of D through φ. We study the case in which n′:=dim V=1 and in general we discuss the case in which n′ is small. The starting point is an analysis of the adjunction map φ using Bogomolov-Reider-Serrano techniques; several results from curve theory are also needed. © 1994 Kluwer Academic Publishers.File in questo prodotto:
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