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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2306.02723 |
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| _version_ | 1866909854593974272 |
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| author | Torelli, Sara |
| author_facet | Torelli, Sara |
| contents | Constant cycle curves on a K3 surface $X$ over $\mathbb{C}$ have been introduced by Huybrechts (2014) as curves whose points all define the same class in the Chow group. In this paper we study correspondences $Z \subseteq X\times X$ over $\mathbb{C}$ acting on the group $\mbox{ccc}(X)$ of cycles generated by irreducible constant cycle curves. We construct for any $n\geq 2$ and any very ample line bundle $L$ a locus $Z_n(L)\subseteq X\times X$ of expected dimension $2$, which yields a correspondence that acts on $\mbox{ccc}(X)$, when it has the expected dimension. We provide examples of $Z_n(L)$ for low $n$ and exhibit one correspondence different from $Z_n(L)$ acting on $\mbox{ccc}(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02723 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Correspondences acting on constant cycle curves on K3 surfaces Torelli, Sara Algebraic Geometry Constant cycle curves on a K3 surface $X$ over $\mathbb{C}$ have been introduced by Huybrechts (2014) as curves whose points all define the same class in the Chow group. In this paper we study correspondences $Z \subseteq X\times X$ over $\mathbb{C}$ acting on the group $\mbox{ccc}(X)$ of cycles generated by irreducible constant cycle curves. We construct for any $n\geq 2$ and any very ample line bundle $L$ a locus $Z_n(L)\subseteq X\times X$ of expected dimension $2$, which yields a correspondence that acts on $\mbox{ccc}(X)$, when it has the expected dimension. We provide examples of $Z_n(L)$ for low $n$ and exhibit one correspondence different from $Z_n(L)$ acting on $\mbox{ccc}(X)$. |
| title | Correspondences acting on constant cycle curves on K3 surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2306.02723 |