Classification of sextic curves in the Fano 3-fold $\mathcal{V}_5$ with rational Galois covers in ${\mathbb P}^3$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917991972601856 |
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| author | Chi, Quo-Shin Xie, Zhenxiao Xu, Yan |
| author_facet | Chi, Quo-Shin Xie, Zhenxiao Xu, Yan |
| contents | In this paper, we classify sextic curves in the Fano $3$-fold $\bf \mathcal{V}_5$ (the smooth quintic del Pezzo $3$-fold) that admit rational Galois covers in the complex ${\mathbb P}^3$. We show that the moduli space of such sextic curves is of complex dimension $2$ through the invariants of the engaged Galois groups for the explicit constructions. This raises the intriguing question of understanding the moduli space of sextic curves in ${\mathcal V}_5$ through their Galois covers in ${\mathbb P}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of sextic curves in the Fano 3-fold $\mathcal{V}_5$ with rational Galois covers in ${\mathbb P}^3$ Chi, Quo-Shin Xie, Zhenxiao Xu, Yan Algebraic Geometry Differential Geometry Representation Theory In this paper, we classify sextic curves in the Fano $3$-fold $\bf \mathcal{V}_5$ (the smooth quintic del Pezzo $3$-fold) that admit rational Galois covers in the complex ${\mathbb P}^3$. We show that the moduli space of such sextic curves is of complex dimension $2$ through the invariants of the engaged Galois groups for the explicit constructions. This raises the intriguing question of understanding the moduli space of sextic curves in ${\mathcal V}_5$ through their Galois covers in ${\mathbb P}^3$. |
| title | Classification of sextic curves in the Fano 3-fold $\mathcal{V}_5$ with rational Galois covers in ${\mathbb P}^3$ |
| topic | Algebraic Geometry Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2504.14168 |