Assuming a canonical basis of the section ring satisfies valuative independence, the metric SYZ conjecture holds for polarised maximal degenerations of compact Calabi-Yau manifolds.
Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi-Yau hypersurfaces
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Valuatively independent bases for H^0(X, L^k) on the Fermat family of cubic curves are constructed for each k using a canonical cost function from the Hessian structure on the essential skeleton.
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Valuative independence and metric SYZ conjecture
Assuming a canonical basis of the section ring satisfies valuative independence, the metric SYZ conjecture holds for polarised maximal degenerations of compact Calabi-Yau manifolds.
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Valuatively independent bases for the Fermat family of cubic curves
Valuatively independent bases for H^0(X, L^k) on the Fermat family of cubic curves are constructed for each k using a canonical cost function from the Hessian structure on the essential skeleton.