Valuatively independent bases are constructed for sections on log CY pairs and regular functions on affine CY pairs, inducing canonical skeleton functions expected to agree with theta tropicalizations.
Li,Degeneration of Calabi-Yau metrics and canonical basis,2505.11087
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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.
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.
Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.
citing papers explorer
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Valuative independence for Calabi--Yau varieties
Valuatively independent bases are constructed for sections on log CY pairs and regular functions on affine CY pairs, inducing canonical skeleton functions expected to agree with theta tropicalizations.
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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.
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What to do with a Ricci-flat Calabi--Yau metric?
Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.