Elementary links from prime Fano threefolds along two lines
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917395364315136 |
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| author | Fujita, Kento |
| author_facet | Fujita, Kento |
| contents | For prime Fano threefolds $X$ of genus $g=12$, $10$ or $9$, and for totally disjoint pairs of lines $Z_1$, $Z_2$ in $X$, we establish links from the blowups of $X$ along $Z_1$ and $Z_2$. If $g=12$, then the links end with the blowups of Fano threefolds of type 2.21 along bi-cubic curves; if $g=10$, then the links end with the blowups of the projectivization of the tangent bundle of the projective plane along genus $2$ bi-quintic curves with a mild condition; if $g=9$, then the links end with conic bundles over the product of two projective lines with the discriminant loci of bidegree $(3,3)$. When $g=12$ or $g=10$, we also establish the converses of the above links. Moreover, we especially focus on the links when $g=12$ and the links are $\mathbb{G}_m$-equivariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Elementary links from prime Fano threefolds along two lines Fujita, Kento Algebraic Geometry 14J45, 14J30, 14J50 For prime Fano threefolds $X$ of genus $g=12$, $10$ or $9$, and for totally disjoint pairs of lines $Z_1$, $Z_2$ in $X$, we establish links from the blowups of $X$ along $Z_1$ and $Z_2$. If $g=12$, then the links end with the blowups of Fano threefolds of type 2.21 along bi-cubic curves; if $g=10$, then the links end with the blowups of the projectivization of the tangent bundle of the projective plane along genus $2$ bi-quintic curves with a mild condition; if $g=9$, then the links end with conic bundles over the product of two projective lines with the discriminant loci of bidegree $(3,3)$. When $g=12$ or $g=10$, we also establish the converses of the above links. Moreover, we especially focus on the links when $g=12$ and the links are $\mathbb{G}_m$-equivariant. |
| title | Elementary links from prime Fano threefolds along two lines |
| topic | Algebraic Geometry 14J45, 14J30, 14J50 |
| url | https://arxiv.org/abs/2604.08097 |