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arXiv · 1712.04635

On a family of negative curves

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

Let $X$ be the blowup of a weighted projective plane at a general point. We study the problem of finite generation of the Cox ring of $X$. Generalizing examples of Srinivasan and Kurano-Nishida, we consider examples of $X$ that contain a negative curve of the class $H-mE$, where $H$ is the class of a divisor pulled back from the weighted projective plane and $E$ is the class of the exceptional curve. For any $m>0$ we construct examples where the Cox ring is finitely generated and examples where it is not.

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Javier González-Anaya, José Luis González, Kalle Karu. 2017-12-13. On a family of negative curves. https://arxiv.org/abs/1712.04635

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