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arXiv · 1810.00508

Constructing non-Mori Dream Spaces from negative curves

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

We study blowups of weighted projective planes at a general point, and more generally blowups of toric surfaces of Picard number one. Based on the positive characteristic methods of Kurano and Nishida, we give a general method for constructing examples of Mori Dream Spaces and non-Mori Dream Spaces among such blowups. Compared to previous constructions, this method uses the geometric properties of the varieties and applies to a number of cases. We use it to fully classify the examples coming from two families of negative curves.

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Javier González-Anaya, José Luis González, Kalle Karu. 2018-10-01. Constructing non-Mori Dream Spaces from negative curves. https://arxiv.org/abs/1810.00508

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