The entropy identity for non-Archimedean test curves

Let XX be a compact Kähler manifold with Kähler form ω\omega, let E1,NA\mathcal{E}^{1,\mathrm{NA}} be the relevant non-Archimedean energy space, and let ellE1,NAell\in\mathcal{E}^{1,\mathrm{NA}}. Set ψ=^\psi=\hat{\ell}. Entropy identity conjecture. One has

EntNA(NA)=Ent()=Ent(ψ).\operatorname{Ent}^{\mathrm{NA}}(\ell^{\mathrm{NA}})=\mathbf{Ent}(\ell)=\operatorname{Ent}(\psi_{\bullet}).

This asserts compatibility of algebraic, test-curve, and singularity-type entropy. The source does not state whether the identity has been proved or disproved.

Sources & referencesView supporting material

Primary source

Mingchen Xia, “Pluripotential-theoretic stability thresholds”, arXiv:2012.12039 (2022).

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