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Classification of Algebraic Surfaces withSectional Genus less than or Equal to Six.II: Ruled Surfaces with dim ϕKx⊗L(x) = l

Published online by Cambridge University Press:  20 November 2018

Elvira Laura Livorni
Elvira Laura Livorni*
Affiliation:
Instituto di Matematica, L'Aguila, Italy
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Let L be a very ample line bundle on a smooth, connected, projective, ruled not rational surface X. We have considered the problem of classifying biholomorphically smooth, connected, projected, ruled, non rational surfaces X with smooth hyperplane section C such that the genus g = g(C) is less than or equal to six and dim where is the map associated to . L. Roth in [10] had given a birational classification of such surfaces. If g = 0 or 1 then X has been classified, see [8].

If g = 2 ≠ hl,0(X) by [12, Lemma (2.2.2) ] it follows that X is a rational surface. Thus we can assume g ≦ 3.

Since X is ruled, h2,0(X) = 0 and

see [4] and [12, p. 390].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 5 , 01 October 1986 , pp. 1110 - 1121
Copyright
Copyright © Canadian Mathematical Society 1986

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