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arXiv · 2503.23382

Monodromy factorizations of lines on del Pezzo surfaces

Mohan Bhupal·Sergey Finashin
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Abstract

We give a list of monodromy factorizations in the pure mapping class group $PMod(T_{d+1})$ 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 $PMod(T_d)$ 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.

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Mohan Bhupal, Sergey Finashin. 2025-03-30. Monodromy factorizations of lines on del Pezzo surfaces. https://arxiv.org/abs/2503.23382

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