Counting Lines on Quartic Surfaces

Abstract

We prove the sharp bound of at most 64 lines on complex projective quartic surfaces (resp. affine quartics) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of singular quartics with many lines.

References in corpus (3)

• Linear subspaces, symbolic powers and Nagata type conjectures
• 64 lines on smooth quartic surfaces
• 112 lines on smooth quartic surfaces (characteristic 3)

Cited by in corpus (4)

• Lines on K3 quartic surfaces in characteristic 2
• Lines on K3-quartics via triangular sets
• Quintic threefolds with triple points
• Secant indices of projective varieties