Lines on K3-quartics via triangular sets

TL;DR

This paper establishes the maximum number of lines on certain complex K3-surfaces and classifies configurations with many lines on smooth quartic surfaces, advancing understanding of algebraic geometry structures.

Contribution

It provides a sharp upper bound for lines on degree four K3-surfaces with singularities and classifies configurations exceeding 48 lines on smooth quartics.

Findings

Maximum of 52 lines on singular degree four K3-surfaces.

Classification of line configurations with over 48 lines on smooth quartics.

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.