Sections of rational elliptic Lefschetz fibrations

Date

2025-03-01

Author

Bhupal, Mohan
Finashin, Sergey

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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.

URI

http://arxiv.org/pdf/2503.23382v1
https://hdl.handle.net/11511/115275

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Department of Mathematics, Article