The cubo-cubic transformation of the smooth quadric fourfold is very special
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910529627357184 |
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| author | Hernández, Jordi |
| author_facet | Hernández, Jordi |
| contents | We classify special self-birational transformations of the smooth quadric threefold and fourfold, $Q^3$ and $Q^4$. It turns out that there is only one such example in each dimension. In the case of $Q^3$, it is given by the linear system of quadrics passing through a rational normal quartic curve. In the case of $Q^4$, it is given by the linear system of cubics passing through a non-minimal K3 surface of degree $10$ with two skew $(-1)$-lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06766 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The cubo-cubic transformation of the smooth quadric fourfold is very special Hernández, Jordi Algebraic Geometry We classify special self-birational transformations of the smooth quadric threefold and fourfold, $Q^3$ and $Q^4$. It turns out that there is only one such example in each dimension. In the case of $Q^3$, it is given by the linear system of quadrics passing through a rational normal quartic curve. In the case of $Q^4$, it is given by the linear system of cubics passing through a non-minimal K3 surface of degree $10$ with two skew $(-1)$-lines. |
| title | The cubo-cubic transformation of the smooth quadric fourfold is very special |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2310.06766 |