Lines on K3-sextics with simple singularities
arXiv:2512.08018
The paper classifies configurations of at least 36 lines on complex K3 sextic surfaces with only A‑D‑E singularities, studies related birational automorphism groups, and shows such surfaces cannot contain a Kummer line configuration, also describing line arrangements on Humbert K3 sextics.
Abstract
We advance our understanding of the configurations of low degree smooth rational curves on (quasi-)polarized complex K3-surfaces. We apply our efficient approach to classify the configurations of at least 36 lines on K3-sextics with at worst A-D-E singularities. Besides, we characterize a certain class of infinite dihedral groups of birational automorphisms of K3-sextics, we show that no K3-sextic can contain a Kummer configuration of lines, and we give a complete account of the line configurations on closest analogue of Kummer K3-octics or quartics, viz. the so-called Humbert K3-sextics.
33 pages and 3 ancillary files. Minor changes in the exposition, extra explanation added. Hyper refs fixed