English

Planar, rational curves over ${\mathbb F}_2$ whose only singularity is a double point

Algebraic Geometry 2026-04-21 v3

Abstract

We exhibit planar, rational curves of large degree over F2{\mathbb F}_2 that have a unique singular point, which has multiplicity 2. In characteristic 0 such curves exist only for degrees up to 66. v.2: references updated and examples of supersingular double planes added. v.3: references updated.

Keywords

Cite

@article{arxiv.2603.04211,
  title  = {Planar, rational curves over ${\mathbb F}_2$ whose only singularity is a double point},
  author = {János Kollár},
  journal= {arXiv preprint arXiv:2603.04211},
  year   = {2026}
}
R2 v1 2026-07-01T11:03:18.672Z