Strict negativity and non-vanishing of Chen--Larson hypergeometric coefficients
Chen and Larson study tautological classes on the strata of holomorphic abelian differentials, where they predict a vanishing result. Using known tautological relations on the moduli space of curves, they reduce this prediction to the non-vanishing of certain coefficients of a quotient of hypergeometric generating series, treating the residue classes $g\equiv0,2\pmod3$ and $g\equiv1\pmod3$ through two separate series; they verify the non-vanishing by computer for small genus. We prove it in general: in both cases the relevant coefficient is non-vanishing for every genus and every stratum,…
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