Lines on quartic surfaces

Abstract

We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56). We also give a complete projective classification of all quartics containing more than 52 lines: all such quartics are projectively rigid. Any value not exceeding 52 can appear as the number of lines of an appropriate quartic.

Cited by in corpus (9)

• Lines on smooth polarized $K3$-surfaces
• Lines in supersingular quartics
• At most 64 lines on smooth quartic surfaces (characteristic 2)
• 24 rational curves on K3 surfaces
• Conics in sextic $K3$-surfaces in ${\mathbb{P}}^4$
• Lines on K3 quartic surfaces in characteristic 3
• Lines on K3-quartics via triangular sets
• Conics in Kummer quartics
• Conics on Barth--Bauer octics