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arXiv · 2412.17036

Mori dream singular $K3$ surfaces

Antonio Laface·Alex Massarenti·William D. Montoya
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Abstract

We take a first step towards the classification of singular Mori dream $K3$ surfaces. We prove that if the Picard lattice of a singular $K3$ surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular $K3$ surfaces, of Picard rank two, being Mori dream is equivalent to contain two negative curves intersecting each other, and apply this result to study Mori dreamness of $K3$ surfaces with a singular point of type $A_n$.

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Antonio Laface, Alex Massarenti, William D. Montoya. 2024-12-22. Mori dream singular $K3$ surfaces. https://arxiv.org/abs/2412.17036

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