Lines on K3-quartics via triangular sets

Abstract

We prove the sharp upper bound of at most $52$ lines on a complex K3-surface of degree four with a non-empty singular locus. We also classify the configurations of more than $48$ lines on smooth complex quartics.

22 pages, extra data available as ancillary files

References in corpus (7)

• Lines on smooth polarized $K3$-surfaces
• Lines on quartic surfaces
• Lines in supersingular quartics
• Smooth models of singular $K3$-surfaces
• Lines on K3 quartic surfaces in characteristic 2
• Symmetries and equations of smooth quartic surfaces with many lines
• Lines on K3 quartic surfaces in characteristic 3