Noether-Lefschetz general complete intersection K3 surfaces over the rationals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908863299584000 |
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| author | Auel, Asher Scheible, Henry |
| author_facet | Auel, Asher Scheible, Henry |
| contents | We prove that the locus of Noether-Lefschetz general polarized K3 surfaces of degree at most 8 defined over the rational numbers is Zariski dense in the moduli space. Previously, this was proved by van Luijk in the quartic case, and it follows from work of Elsenhans and Jahnel in the degree 2 case. Innovations on their methods, and employing Mukai's Hodge isogeny, suffices to handle the degree 8 case. New methods allow us to deal with the case of degree 6. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03253 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noether-Lefschetz general complete intersection K3 surfaces over the rationals Auel, Asher Scheible, Henry Algebraic Geometry Number Theory 14J28, 14J20, 14C22, 14G05 We prove that the locus of Noether-Lefschetz general polarized K3 surfaces of degree at most 8 defined over the rational numbers is Zariski dense in the moduli space. Previously, this was proved by van Luijk in the quartic case, and it follows from work of Elsenhans and Jahnel in the degree 2 case. Innovations on their methods, and employing Mukai's Hodge isogeny, suffices to handle the degree 8 case. New methods allow us to deal with the case of degree 6. |
| title | Noether-Lefschetz general complete intersection K3 surfaces over the rationals |
| topic | Algebraic Geometry Number Theory 14J28, 14J20, 14C22, 14G05 |
| url | https://arxiv.org/abs/2603.03253 |