Prediction for the moving slope of the moduli space of principally polarized abelian fivefolds

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Let A‾5\overline{\mathcal{A}}_5 be a compactification of the moduli space of principally polarized abelian fivefolds, and let s′(A‾5)s'(\overline{\mathcal{A}}_5) denote its moving slope. Since the divisor N0′‾\overline{N_0'} is rigid, one has s′(A‾5)>s(N0′‾)s'(\overline{\mathcal{A}}_5)>s(\overline{N_0'}). Moving-slope prediction.

s′(A‾5)=709.s'(\overline{\mathcal{A}}_5)=\frac{70}{9}.

This predicts the value of the moving slope and refines the preceding lower bound arising from the rigid divisor N0′‾\overline{N_0'}; the supplied text does not state whether the prediction has been proved or remains open.

References

Primary source

Gavril Farkas, Samuel Grushevsky, Riccardo Salvati Manni and Alessandro Verra, “Singularities of theta divisors and the geometry of A_5”, arXiv:1112.6285 (2022).

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