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Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles générique. (A conjecture for the cohomology of divisors on generic rational surfaces). (French) Zbl 0686.14013
Let \(S_ r\) be the blowing-up of \({\mathbb{P}}^ 2\) at r general points. Here it is given a very precise conjecture about the cohomology of line bundles on \(S_ r\). It would be nice to have similar (or even much weaker) conjectures about other surfaces and/or to know more about the blowing-up at not too general points. The paper contains also a proof of an interesting special case of the conjecture.
Reviewer: E.Ballico

14F99 (Co)homology theory in algebraic geometry
14M20 Rational and unirational varieties
14C22 Picard groups
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