Conics in Kummer quartics

Abstract

We classify the configurations of lines and conics in smooth Kummer quartics, assuming that all $16$ Kummer divisors map to conics. We show that the number of conics on such a quartic is at most $800$.

References in corpus (8)

• 64 lines on smooth quartic surfaces
• Geography of irreducible plane sextics
• Lines on smooth polarized $K3$-surfaces
• Lines on quartic surfaces
• K3 surfaces with maximal finite automorphism groups containing $M\_20$
• 800 conics in a smooth quartic surface
• Counting lines on surfaces, especially quintics
• Conics in sextic $K3$-surfaces in ${\mathbb{P}}^4$