Sections of rational elliptic Lefschetz fibrations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913766491291648 |
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| author | Bhupal, Mohan Finashin, Sergey |
| author_facet | Bhupal, Mohan Finashin, Sergey |
| contents | We give a list of monodromy factorizations in the pure mapping class group $Mod(T_{d+1})$ of a torus with d+1 marked points that represent lines on a del Pezzo surface Y of degree $d\le4$. These factorizations are lifts of a certain fixed monodromy factorization in $Mod(T_d)$ that represents Y. In the case d=1, discussed in more detail, we give an explicit correspondence between such factorizations and the 240 roots of $E_8=K^\perp$, the orthogonal complement in $H_2(Y)$ of the canonical class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_23382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sections of rational elliptic Lefschetz fibrations Bhupal, Mohan Finashin, Sergey Algebraic Geometry Geometric Topology 57K20 (Primary) 57K43, 14J27 (Secondary) We give a list of monodromy factorizations in the pure mapping class group $Mod(T_{d+1})$ of a torus with d+1 marked points that represent lines on a del Pezzo surface Y of degree $d\le4$. These factorizations are lifts of a certain fixed monodromy factorization in $Mod(T_d)$ that represents Y. In the case d=1, discussed in more detail, we give an explicit correspondence between such factorizations and the 240 roots of $E_8=K^\perp$, the orthogonal complement in $H_2(Y)$ of the canonical class. |
| title | Sections of rational elliptic Lefschetz fibrations |
| topic | Algebraic Geometry Geometric Topology 57K20 (Primary) 57K43, 14J27 (Secondary) |
| url | https://arxiv.org/abs/2503.23382 |