Geodesic
Rational Surfaces of Kodaira Type IV
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 741-750

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We study the geometry of a rational surface of Kodaira type IV by giving the nature of its integral curves of self-intersection less than zero, in particular we show that they are smooth and rational. Hence, under a reasonable assumption, we prove the finite generation of its monoid of effective divisor classes and in almost all cases its anticanonical complete linear system is of projective dimension zero and of self- intersection strictly negative. Furthermore, we show that if this condition is not fulfilled, the monoid may fail to be finitely generated. 
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     title = {Rational {Surfaces} of {Kodaira} {Type} {IV}},
     journal = {Bollettino della Unione matematica italiana},
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Failla, Gioia; Lahyane, Mustapha; Molica Bisci, Giovanni. Rational Surfaces of Kodaira Type IV. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 741-750. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a18/