On large configurations of lines on quartic surfaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912455806943232 |
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| author | Degtyarev, Alex Rams, Sławomir |
| author_facet | Degtyarev, Alex Rams, Sławomir |
| contents | We estimate the number of lines on a non-K3 quartic surface. Such a surface with only isolated double point(s) contains at most twenty lines; this bound is attained by a unique configuration of lines and by a surface with a certain limited set of singularities. We have similar itemized bounds for other types of non-simple singularities, which culminate in at most 31 lines on a non-K3 quartic not ruled by lines; this bound is only attained on the quartic monoids described by K.~Rohn. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On large configurations of lines on quartic surfaces Degtyarev, Alex Rams, Sławomir Algebraic Geometry 14J26 14N25 We estimate the number of lines on a non-K3 quartic surface. Such a surface with only isolated double point(s) contains at most twenty lines; this bound is attained by a unique configuration of lines and by a surface with a certain limited set of singularities. We have similar itemized bounds for other types of non-simple singularities, which culminate in at most 31 lines on a non-K3 quartic not ruled by lines; this bound is only attained on the quartic monoids described by K.~Rohn. |
| title | On large configurations of lines on quartic surfaces |
| topic | Algebraic Geometry 14J26 14N25 |
| url | https://arxiv.org/abs/2506.22733 |