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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Mustapha Lahyane 1
@article{CRMATH_2004__338_11_873_0, author = {Mustapha Lahyane}, title = {Exceptional curves on rational surfaces having {\protect\emph{K}\protect\textsuperscript{2}\ensuremath{\geqslant}0}}, journal = {Comptes Rendus. Math\'ematique}, pages = {873--878}, publisher = {Elsevier}, volume = {338}, number = {11}, year = {2004}, doi = {10.1016/j.crma.2004.03.029}, language = {en}, }
Mustapha Lahyane. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.029/
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