Lines in supersingular quartics

Abstract

We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the number of lines is at most 60 in both cases. We also give a complete classification of large configurations of lines.

Final version accepted for publication. Theorem 1.1 had to be stated in a weaker version

References in corpus (2)

• Lines on quartic surfaces
• At most 64 lines on smooth quartic surfaces (characteristic 2)

Cited by in corpus (8)

• Lines on smooth polarized $K3$-surfaces
• Smooth models of singular $K3$-surfaces
• Counting lines on surfaces, especially quintics
• Lines on K3 quartic surfaces in characteristic 2
• Symmetries and equations of smooth quartic surfaces with many lines
• Lines on K3-quartics via triangular sets
• Counting Lines with Vinberg's algorithm
• Conics on Barth--Bauer octics