I am trying to find a (smooth) compact complex surface $X$ so that the set of irreducible curves $C$ on $X$ for which $C.C<0$ is infinite. Do any of you know of an example. Thanks.
Blow up $\mathbb P^2$ at 9 points. See e.g. Hartshorne exercise 5.4.15e) and the reference there.
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4 years ago