# Non-existence of negative curves

@inproceedings{GonzalezAnaya2021NonexistenceON, title={Non-existence of negative curves}, author={Javier Gonz'alez-Anaya and Jos'e Luis Gonz'alez and Kalle Karu}, year={2021} }

Let X be a projective toric surface of Picard number one blown up at a general point. We bring an infinite family of examples of such Xwhose Kleiman-Mori cone of curves is not closed: there is no negative curve generating one of the two boundary rays of the cone. These examples are related to Nagata’s conjecture and rationality of Seshadri constants.

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