Algebraic Geometry
Exceptional curves on rational surfaces having K2⩾0
Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 873-878.

We characterize the rational surfaces X which have a finite number of (−1)-curves under the assumption that −KX is nef, where KX is a canonical divisor on X, and has self-intersection zero. We prove also that if −KX is not nef and has self-intersection zero, then X has a finite number of (−1)-curves.

Nous caractérisons les surfaces rationnelles X qui ont un nombre fini de (−1)-courbes sous les conditions que −KX soit nef, KX étant un diviseur canonique sur X, et que KX2 soit égal à zero. Nous prouvons aussi que si −KX n'est pas nef et de carré nul, alors X a un nombre fini de (−1)-courbes.

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Published online:
DOI: 10.1016/j.crma.2004.03.029
Lahyane, Mustapha 1

1 Depto. de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Valladolid, Valladolid 47005, Spain
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Lahyane, Mustapha. Exceptional curves on rational surfaces having K2⩾0. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 873-878. doi : 10.1016/j.crma.2004.03.029. http://www.numdam.org/articles/10.1016/j.crma.2004.03.029/

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