64 lines on smooth quartic surfaces
Algebraic Geometry
2016-11-14 v5 Number Theory
Abstract
Let k be a field of characteristic other than 2,3. We prove that there are no geometrically smooth quartic surfaces in IP^3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on a smooth quartic.
Keywords
Cite
@article{arxiv.1212.3511,
title = {64 lines on smooth quartic surfaces},
author = {Slawomir Rams and Matthias Schuett},
journal= {arXiv preprint arXiv:1212.3511},
year = {2016}
}
Comments
19 pages; v5: assumption for Prop. 7.1 added, main results unaffected