Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Degtyarev, Alex, Rams, Sławomir
Institution: Jagiellonian University
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7114792940
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