Higher Chow cycles on K3 surfaces attached to plane quartics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914915010215936 |
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| author | Sato, Ken |
| author_facet | Sato, Ken |
| contents | In this paper, we give an explicit construction of higher Chow cycles of type $(2,1)$ on $K3$ surfaces obtained as quadruple coverings of the projective plane ramified along smooth quartics. The construction uses a pair of bitangents of the quartics. We prove that the higher Chow cycles generate a rank 2 subgroup in the indecomposable part of the higher Chow group for very general members, by using a specialization argument and an explicit computation of the regulator map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Chow cycles on K3 surfaces attached to plane quartics Sato, Ken Algebraic Geometry 14C15, 14J28 In this paper, we give an explicit construction of higher Chow cycles of type $(2,1)$ on $K3$ surfaces obtained as quadruple coverings of the projective plane ramified along smooth quartics. The construction uses a pair of bitangents of the quartics. We prove that the higher Chow cycles generate a rank 2 subgroup in the indecomposable part of the higher Chow group for very general members, by using a specialization argument and an explicit computation of the regulator map. |
| title | Higher Chow cycles on K3 surfaces attached to plane quartics |
| topic | Algebraic Geometry 14C15, 14J28 |
| url | https://arxiv.org/abs/2408.09102 |