Explicit equations of 800 conics on a Barth-Bauer quartic

TL;DR

This paper provides explicit equations for 800 conics on a specific K3 surface, setting a new record for the number of irreducible conics on a smooth quartic in projective space.

Contribution

It presents the first explicit equations for such a large set of conics on a Mukai's quartic, advancing the understanding of conic configurations on K3 surfaces.

Findings

800 conics explicitly described on a Mukai's quartic

Record number of irreducible conics on a smooth quartic

Enhanced understanding of conic arrangements on K3 surfaces

Abstract

We present equations of $800$ conics on a Mukai's smooth quartic which is an explicit model of a K3 surface recently considered by Alex Degtyarev. The number $800$ is a current record for the number of irreducible conics on a smooth quartic in ordinary projective space.