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arXiv · 2110.13333

Non-existence of negative curves

Javier González-Anaya·José Luis González·Kalle Karu
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Abstract

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 $X$ whose 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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Javier González-Anaya, José Luis González, Kalle Karu. 2021-10-26. Non-existence of negative curves. https://arxiv.org/abs/2110.13333

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