English

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 K3K3 surfaces. We prove that if the Picard lattice of a singular K3K3 surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular K3K3 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 K3K3 surfaces with a singular point of type AnA_n.

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}
}

Comments

15 pages

R2 v1 2026-06-28T20:45:39.909Z