Xiao's hyperellipticity conjecture for Lefschetz fibrations
Xiao's hyperellipticity conjecture for Lefschetz fibrations
Let be a genus- Lefschetz fibration with slope , and call hyperelliptic when its monodromy lies in the hyperelliptic mapping class group. Xiao's hyperellipticity conjecture. If
then is hyperelliptic. The source says that this conjecture is raised for holomorphic Lefschetz fibrations over curves of any nonnegative genus. It also explains that the paper gives a counterexample in the broader Lefschetz-fibration setting, so the claim must be understood with Xiao's holomorphic hypotheses.
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Sources & referencesView supporting material
Primary source
Tulin Altunoz and Adalet Cengel, “Constructing Lefschetz Fibrations with Arbitrary Slope”, arXiv:2512.03714 (2026).
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