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arXiv · 1110.0722

On the influence of the Segre Problem on the Mori cone of blown-up surfaces

Fulvio Di Sciullo
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Abstract

We propose a generalization of SHGH Conjectures to a smooth projective surface Y: the so called Segre Problem. The study of linear systems on Y can be translated in terms of the Mori cone of the blow up $X = Bl_r Y$ at $r$ general points. Generalizing a result by de Fernex, we prove that if Segre Problem holds true, then a part of the Mori cone of $X$ does coincide with a part of the positive cone of $X$.

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Fulvio Di Sciullo. 2012-06-18. On the influence of the Segre Problem on the Mori cone of blown-up surfaces. https://arxiv.org/abs/1110.0722

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