On large configurations of lines on quartic surfaces
Algebraic Geometry
2025-07-01 v1
Abstract
We estimate the number of lines on a non-K3 quartic surface. Such a surface with only isolated double point(s) contains at most twenty lines; this bound is attained by a unique configuration of lines and by a surface with a certain limited set of singularities. We have similar itemized bounds for other types of non-simple singularities, which culminate in at most 31 lines on a non-K3 quartic not ruled by lines; this bound is only attained on the quartic monoids described by K.~Rohn.
Keywords
Cite
@article{arxiv.2506.22733,
title = {On large configurations of lines on quartic surfaces},
author = {Alex Degtyarev and Sławomir Rams},
journal= {arXiv preprint arXiv:2506.22733},
year = {2025}
}