Conics in sextic $K3$-surfaces in ${\mathbb{P}}^4$

Abstract

We prove that the maximal number of conics in a smooth sextic $K3$-surface $X\subset {\mathbb{P}}^4$ is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible.

Final version appearing in Nagoya Math. J

Cited by in corpus (2)

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• Conics on Barth--Bauer octics