Conics on smooth quartic surfaces

TL;DR

This paper establishes the maximum number of conics on smooth quartic surfaces as 800, classifies quartics with many conics, and discusses real conics count bounds.

Contribution

It proves the maximum number of conics on smooth quartic surfaces is 800 and classifies quartics with at least 720 conics, providing new bounds and classifications.

Findings

Maximum of 800 conics on a smooth quartic surface

Unique quartic achieving the maximum

Bounds for real conics between 656 and 718

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.