Geodesic
Vertically of (-1)-Lines in Scrolls Over Smooth Surfaces
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 236-239

Voir la notice de l'article provenant de la source Cambridge University Press

Let S be a smooth surface contained as an ample divisor in a smooth complex projective threefold X, which is a P 1 -bundle, and assume that induces OP 1 (1) on the fibres of X. The following fact is proven. The restriction to S of the bundle projection of X is exactly the reduction morphism of the pair provided that this one is not a conic bundle. The proof is very simple and does not involve any consideration on the nefness of the adjoint bundle Some applications of the proof are given.
DOI : 10.4153/CMB-1991-038-3
Mots-clés : 14C20, 14J30., ample line bundle, scroll, quadric bundle, adjunction theory. 
Lanteri, Antonio. Vertically of (-1)-Lines in Scrolls Over Smooth Surfaces. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 236-239. doi: 10.4153/CMB-1991-038-3
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