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EnglishAbstract 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.
| Titolo: | Rational surfaces with anticanonical divisor not reduced | |
| Autori: | ||
| Data di pubblicazione: | 2013 | |
| Rivista: | ||
| Handle: | http://hdl.handle.net/20.500.12318/8288 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/20.500.12318/8288
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