Mori dream singular $K3$ surfaces
Algebraic Geometry
2024-12-24 v1 Number Theory
Abstract
We take a first step towards the classification of singular Mori dream surfaces. We prove that if the Picard lattice of a singular surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular 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 surfaces with a singular point of type .
Keywords
Cite
@article{arxiv.2412.17036,
title = {Mori dream singular $K3$ surfaces},
author = {Antonio Laface and Alex Massarenti and William D. Montoya},
journal= {arXiv preprint arXiv:2412.17036},
year = {2024}
}
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15 pages