112 lines on smooth quartic surfaces (characteristic 3)
Algebraic Geometry
2016-11-14 v2
Abstract
Over a field k of characteristic 3, we prove that there are no smooth quartic surfaces S in IP^3 with more than 112 lines. Moreover, the surface with 112 lines is projectively equivalent over k-bar to the Fermat quartic. As a key ingredient, we derive a characteristic free upper bound for the number of lines met by a quadric on a smooth quartic surface.
Keywords
Cite
@article{arxiv.1409.7485,
title = {112 lines on smooth quartic surfaces (characteristic 3)},
author = {Slawomir Rams and Matthias Schuett},
journal= {arXiv preprint arXiv:1409.7485},
year = {2016}
}
Comments
11 pages; v2: minor edits following referee's comments