Rational Surfaces with Anticanonical Divisor not Reduced
2013 ◽
Vol 21
(3)
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pp. 229-240
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AbstractWe 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
1995 ◽
Vol 117
(1)
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pp. 161-163
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2016 ◽
Vol 152
(6)
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pp. 1198-1224
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Keyword(s):
2007 ◽
Vol 143
(3)
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pp. 579-605
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Keyword(s):