64 lines on smooth quartic surfaces

Abstract

Let k be a field of characteristic other than 2,3. We prove that there are no geometrically smooth quartic surfaces in IP^3 with more than 64 lines. As a key step, we derive the sharp bound that any line meets at most 20 other lines on a smooth quartic.

19 pages; v5: assumption for Prop. 7.1 added, main results unaffected

References in corpus (1)

• On quartics with lines of the second kind

Cited by in corpus (13)

• 112 lines on smooth quartic surfaces (characteristic 3)
• Lines on smooth polarized $K3$-surfaces
• Lines on quartic surfaces
• Lines in supersingular quartics
• Counting Lines on Quartic Surfaces
• The maximum number of lines lying on a K3 quartic surface
• Lines on K3 quartic surfaces in 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