The maximum number of lines lying on a K3 quartic surface

Abstract

We show that there cannot be more than 64 lines on a quartic surface admitting isolated rational double points over an algebraically closed field of characteristic $p\ne 2,3$, thus extending Segre--Rams--Schütt theorem. Our proof offers a deeper insight into the triangle-free case and takes advantage of a special configuration of lines, thereby avoiding the technique of the flecnodal divisor. We provide several examples of non-smooth K3 quartic surfaces with many lines.

31 pages, 3 tables, 1 figure

References in corpus (3)

• 64 lines on smooth quartic surfaces
• 112 lines on smooth quartic surfaces (characteristic 3)
• On quartics with lines of the second kind

Cited by in corpus (4)

• At most 64 lines on smooth quartic surfaces (characteristic 2)
• Lines on K3 quartic surfaces in characteristic 3
• Lines on K3-quartics via triangular sets
• Conics on Barth--Bauer octics