English

At most 64 lines on smooth quartic surfaces (characteristic 2)

Algebraic Geometry 2019-11-13 v2 Number Theory

Abstract

Let K be a field of characteristic 2. We give a geometric proof that there are no smooth quartic surfaces in IP^3 with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains the record in characteristic 2.

Keywords

Cite

@article{arxiv.1512.01358,
  title  = {At most 64 lines on smooth quartic surfaces (characteristic 2)},
  author = {Slawomir Rams and Matthias Schütt},
  journal= {arXiv preprint arXiv:1512.01358},
  year   = {2019}
}

Comments

16 pages; v2: minor additions and edits, reference to 1604.05836 added

R2 v1 2026-06-22T12:01:27.148Z