Conics on smooth quartic surfaces
Algebraic Geometry
2026-02-12 v2
Abstract
We prove that the maximal number of conics, a priori irreducible of reducible, on a smooth spatial quartic surface is 800, realized by a unique quartic. We also classify quartics with many (at least 720) conics. The maximal number of real conics on a real quartics is between 656 and 718.
Keywords
Cite
@article{arxiv.2407.00493,
title = {Conics on smooth quartic surfaces},
author = {Alex Degtyarev},
journal= {arXiv preprint arXiv:2407.00493},
year = {2026}
}
Comments
Cosmetic changes, refs added, typos corrected, GAP code uploaded