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arXiv · 2512.08018

Lines on K3-sextics with simple singularities

Alex Degtyarev·Sławomir Rams
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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.

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Alex Degtyarev, Sławomir Rams. 2025-12-08. Lines on K3-sextics with simple singularities. https://arxiv.org/abs/2512.08018

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