Xiao's hyperellipticity conjecture for Lefschetz fibrations

From papers

Let ff be a genus-gg Lefschetz fibration with slope λf\lambda_f, and call ff hyperelliptic when its monodromy lies in the hyperelliptic mapping class group. Xiao's hyperellipticity conjecture. If

λf=44g,\lambda_f=4-\frac{4}{g},

then ff 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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