Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces


Abstract in English

We consider rational surfaces $Z$ defined by divisorial valuations $ u$ of Hirzebruch surfaces. We introduce the concepts of non-positivity and negativity at infinity for these valuations and prove that these concepts admit nice local and global equivalent conditions. In particular we prove that, when $ u$ is non-positive at infinity, the extremal rays of the cone of curves of $Z$ can be explicitly given.

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