On K3 surfaces of Picard rank 14
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866918022307905536 |
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| author | Clingher, Adrian Malmendier, Andreas |
| author_facet | Clingher, Adrian Malmendier, Andreas |
| contents | We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H \oplus E_8(-1) \oplus A_1(-1)^{\oplus 4}$, $H \oplus E_8(-1) \oplus D_4(-1)$, and $H \oplus D_8(-1) \oplus D_4(-1)$. As part of our study, we provide birational models for these surfaces as quartic projective hypersurfaces and describe the associated coarse moduli spaces in terms of suitable modular invariants. Additionally, we explore the connection between these families and dual K3 families related via the Nikulin construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_09635 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On K3 surfaces of Picard rank 14 Clingher, Adrian Malmendier, Andreas Algebraic Geometry 14J27, 14J28, 14J15, 14D22 We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank-fourteen, 2-elementary lattices. Three such lattices exist, namely $H \oplus E_8(-1) \oplus A_1(-1)^{\oplus 4}$, $H \oplus E_8(-1) \oplus D_4(-1)$, and $H \oplus D_8(-1) \oplus D_4(-1)$. As part of our study, we provide birational models for these surfaces as quartic projective hypersurfaces and describe the associated coarse moduli spaces in terms of suitable modular invariants. Additionally, we explore the connection between these families and dual K3 families related via the Nikulin construction. |
| title | On K3 surfaces of Picard rank 14 |
| topic | Algebraic Geometry 14J27, 14J28, 14J15, 14D22 |
| url | https://arxiv.org/abs/2009.09635 |