Conics on Barth--Bauer octics
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911991583473664 |
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| author | Degtyarev, Alex |
| author_facet | Degtyarev, Alex |
| contents | We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by $176$ and show that there is a unique surface with $176$ conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane (ramified at a smooth sextic curve) that contains $8910$ smooth conics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06966 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Conics on Barth--Bauer octics Degtyarev, Alex Algebraic Geometry 14J28, 14N25 We analyze the configurations of conics and lines on a special class of Kummer octic surfaces. In particular, we bound the number of conics by $176$ and show that there is a unique surface with $176$ conics, all irreducible: it admits a faithful action of one of the Mukai groups. Therefore, we also discuss conics and lines on Mukai surfaces: we discover a double plane (ramified at a smooth sextic curve) that contains $8910$ smooth conics. |
| title | Conics on Barth--Bauer octics |
| topic | Algebraic Geometry 14J28, 14N25 |
| url | https://arxiv.org/abs/2210.06966 |