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Irreducibility and degree of the logarithmic discriminant of M_{0,n}

Show that the logarithmic discriminant of the moduli space M_{0,n} is an irreducible hypersurface and determine its degree.

References

Show that the logarithmic discriminant of the moduli space $\mathcal{M}_{0,n}$ is an irreducible hypersurface, and determine its degree. \quad Conjecture 1.

What is Positive Geometry? (Ranestad et al., 18 Feb 2025) in Section “Open questions”: Problem [Kayser]