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

Let A5\overline{\mathcal{A}}_5 be a compactification of the moduli space of principally polarized abelian fivefolds, and let s(A5)s'(\overline{\mathcal{A}}_5) denote its moving slope. Since the divisor N0\overline{N_0'} is rigid, one has s(A5)>s(N0)s'(\overline{\mathcal{A}}_5)>s(\overline{N_0'}). Moving-slope prediction.

s(A5)=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.

Sources & referencesView supporting material

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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