Symmetries and equations of smooth quartic surfaces with many lines

Abstract

We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.

22 pages, the last unknown quartic surface with more than 52 lines has been added

References in corpus (2)

• Lines in supersingular quartics
• Smooth models of singular $K3$-surfaces

Cited by in corpus (2)

• Lines on K3 quartic surfaces in characteristic 3
• Lines on K3-quartics via triangular sets