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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.08399 |
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| _version_ | 1866912882404360192 |
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| author | Selvaggi, Ian |
| author_facet | Selvaggi, Ian |
| contents | Given a smooth projective variety $X$ over an algebraically closed field $k$, we compute the Chow ring of the Hilbert scheme of three points on $X$, $\operatorname{Hilb}^3(X)$, as an algebra with generators and relations over the Chow ring of $X\times\operatorname{Sym}^2(X)$. If in addition the characteristic of $k$ is zero, we extend the computation to the quasi-projective case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08399 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Chow Ring of the Hilbert Cube Selvaggi, Ian Algebraic Geometry Given a smooth projective variety $X$ over an algebraically closed field $k$, we compute the Chow ring of the Hilbert scheme of three points on $X$, $\operatorname{Hilb}^3(X)$, as an algebra with generators and relations over the Chow ring of $X\times\operatorname{Sym}^2(X)$. If in addition the characteristic of $k$ is zero, we extend the computation to the quasi-projective case. |
| title | The Chow Ring of the Hilbert Cube |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.08399 |