English

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

R2 v1 2026-06-28T17:23:43.311Z