Lines on K3-sextics with simple singularities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915661916143616 |
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| author | Degtyarev, Alex Rams, Sławomir |
| author_facet | Degtyarev, Alex Rams, Sławomir |
| contents | 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. As an unexpected outcome of the further analysis of configurations of lines, we characterize a certain class of infinite dihedral groups of birational automorphisms of K3-sextics. Besides, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lines on K3-sextics with simple singularities Degtyarev, Alex Rams, Sławomir Algebraic Geometry Primary: 14J28, Secondary: 14N25 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. As an unexpected outcome of the further analysis of configurations of lines, we characterize a certain class of infinite dihedral groups of birational automorphisms of K3-sextics. Besides, 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. |
| title | Lines on K3-sextics with simple singularities |
| topic | Algebraic Geometry Primary: 14J28, Secondary: 14N25 |
| url | https://arxiv.org/abs/2512.08018 |