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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2509.21069 |
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| _version_ | 1866918147973447680 |
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| author | Lee, Ju A |
| author_facet | Lee, Ju A |
| contents | In this article, we present a differential topological construction of symplectic Lefschetz pencils of genus $\frac{(d-1)(d-2)}{2}$ with $d^2$ base points and $3(d-1)^2$ critical points for arbitrary $d\geq 4$, analogous to the holomorphic Lefschetz pencils of curves of degree $d$ in $\mathbb{C}P^2$. Moreover, for the case $d=4$, we derive an explicit monodromy factorization of the genus $3$ holomorphic Lefschetz pencil on $\mathbb{C}P^2$ based on the braid monodromy technique and prove that it can also be topologically constructed by breeding the monodromy relations of the genus $1$ holomorphic Lefschetz pencils. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lefschetz pencils on a complex projective plane from a topological viewpoint Lee, Ju A Geometric Topology 57R22, 57R55, 20F12, 57M07 In this article, we present a differential topological construction of symplectic Lefschetz pencils of genus $\frac{(d-1)(d-2)}{2}$ with $d^2$ base points and $3(d-1)^2$ critical points for arbitrary $d\geq 4$, analogous to the holomorphic Lefschetz pencils of curves of degree $d$ in $\mathbb{C}P^2$. Moreover, for the case $d=4$, we derive an explicit monodromy factorization of the genus $3$ holomorphic Lefschetz pencil on $\mathbb{C}P^2$ based on the braid monodromy technique and prove that it can also be topologically constructed by breeding the monodromy relations of the genus $1$ holomorphic Lefschetz pencils. |
| title | Lefschetz pencils on a complex projective plane from a topological viewpoint |
| topic | Geometric Topology 57R22, 57R55, 20F12, 57M07 |
| url | https://arxiv.org/abs/2509.21069 |