Notes on symplectic action on $(2,1)$-cycles on $K3$ surfaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916953043501056 |
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| author | Sato, Ken |
| author_facet | Sato, Ken |
| contents | In this paper, we propose and study a conjecture that symplectic automorphisms of a $K3$ surface $X$ act trivially on the indecomposable part $\mathrm{CH}^2(X,1)_{\mathrm{ind}}\otimes \mathbb{Q}$ of Bloch's higher Chow group. This is a higher Chow analogue of Huybrechts' conjecture on the symplectic action on $0$-cycles. We give several partial results verifying our conjecture, some conditional and some unconditional. Our unconditional results include the full proof for Kummer surfaces of product type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Notes on symplectic action on $(2,1)$-cycles on $K3$ surfaces Sato, Ken Algebraic Geometry 14C25, 14J28 In this paper, we propose and study a conjecture that symplectic automorphisms of a $K3$ surface $X$ act trivially on the indecomposable part $\mathrm{CH}^2(X,1)_{\mathrm{ind}}\otimes \mathbb{Q}$ of Bloch's higher Chow group. This is a higher Chow analogue of Huybrechts' conjecture on the symplectic action on $0$-cycles. We give several partial results verifying our conjecture, some conditional and some unconditional. Our unconditional results include the full proof for Kummer surfaces of product type. |
| title | Notes on symplectic action on $(2,1)$-cycles on $K3$ surfaces |
| topic | Algebraic Geometry 14C25, 14J28 |
| url | https://arxiv.org/abs/2509.13491 |