an:04123870
Zbl 0686.14013
Hirschowitz, Andr??
Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles g??n??rique. (A conjecture for the cohomology of divisors on generic rational surfaces)
FR
J. Reine Angew. Math. 397, 208-213 (1989).
00154154
1989
j
14F99 14M20 14C22
rational surfaces; divisor; cohomology of line bundles; blowing-up
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.
E.Ballico