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Vertically of (-1)-Lines in Scrolls Over Smooth Surfaces

Published online by Cambridge University Press:  20 November 2018

Antonio Lanteri
Antonio Lanteri*
Affiliation:
Dipartimento di Matematica "F. Enriques"-Université Via C. Saldini 50 1-20133 Milano, Italy
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Abstract

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Let S be a smooth surface contained as an ample divisor in a smooth complex projective threefold X, which is a P1 -bundle, and assume that induces OP1 (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.

Keywords

14C2014J30.ample line bundlescrollquadric bundleadjunction theory.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 236 - 239
Copyright
Copyright © Canadian Mathematical Society 1991

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