Abstract We prove the finite generation of the monoid of effective divisor classes on a smooth projective rational surface X endowed with an anticanonical divisor such that all its irreducible components are of multiplicity one except one which has multiplicity two. In almost all cases, the self-intersection of a canonical divisor KX on X is strictly negative, hence KX is neither ample nor numerically effective. In particular, X is not a Del Pezzo surface. Furthermore, it is shown that the first cohomology group of a numerically effective divisor vanishes; as a consequence, we determine the dimension of the complete linear system associated to any given divisor on X.

Rational surfaces with anticanonical divisor not reduced / Cerda Rodriguez, J A; Failla, Gioia; Lahyane, M; Moreno-Mejia, I; Osuna-Castro, O. - In: ANALELE UNIVERSITAţII OVIDIUS CONSTANTA. SERIA MATEMATICA. - ISSN 1224-1784. - 21:3(2013), pp. 229-240. [10.2478/auom-2013-0055]

Rational surfaces with anticanonical divisor not reduced

FAILLA, Gioia;
2013-01-01

Abstract

Abstract We prove the finite generation of the monoid of effective divisor classes on a smooth projective rational surface X endowed with an anticanonical divisor such that all its irreducible components are of multiplicity one except one which has multiplicity two. In almost all cases, the self-intersection of a canonical divisor KX on X is strictly negative, hence KX is neither ample nor numerically effective. In particular, X is not a Del Pezzo surface. Furthermore, it is shown that the first cohomology group of a numerically effective divisor vanishes; as a consequence, we determine the dimension of the complete linear system associated to any given divisor on X.
2013
Rational surfaces, Blowing-up,; Monoid of effective divisor classes; ,
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/8288
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