Topological and arithmetic characteristics about products of projective lines with complex tori
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910023790100480 |
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| author | Mo, Jia-Li Amram, Meirav Gong, Cheng |
| author_facet | Mo, Jia-Li Amram, Meirav Gong, Cheng |
| contents | In this paper, we study non-planar degeneracies with cylindrical configurations. They could be constructed by the product $\mathbb{CP}^1 \times T$ of the projective plane and a complex torus with embedding $(m,n)$. We prove that their fundamental groups of Galois covers have an abelian subgroup of rank $m(2n-1)$ respectively, and the irregularity of these surfaces are at least $2mn-1$. Furthermore, we also use Chern numbers to compute the index of such surfaces and classify them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14745 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological and arithmetic characteristics about products of projective lines with complex tori Mo, Jia-Li Amram, Meirav Gong, Cheng Algebraic Geometry 05E16, 14J10, 14J80, 20F55 In this paper, we study non-planar degeneracies with cylindrical configurations. They could be constructed by the product $\mathbb{CP}^1 \times T$ of the projective plane and a complex torus with embedding $(m,n)$. We prove that their fundamental groups of Galois covers have an abelian subgroup of rank $m(2n-1)$ respectively, and the irregularity of these surfaces are at least $2mn-1$. Furthermore, we also use Chern numbers to compute the index of such surfaces and classify them. |
| title | Topological and arithmetic characteristics about products of projective lines with complex tori |
| topic | Algebraic Geometry 05E16, 14J10, 14J80, 20F55 |
| url | https://arxiv.org/abs/2602.14745 |