Valuative independence for Calabi--Yau varieties
Algebraic Geometry
2026-05-01 v1 Differential Geometry
Abstract
We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular functions on an affine CY pair with maximal boundary. While the bases are not in general unique, they induce canonical functions on the respective skeletons and are expected to agree with tropicalizations of theta functions when they exist. The proof uses techniques from the study of higher rank degenerations in K-stability.
Keywords
Cite
@article{arxiv.2604.27890,
title = {Valuative independence for Calabi--Yau varieties},
author = {Harold Blum and Yuchen Liu},
journal= {arXiv preprint arXiv:2604.27890},
year = {2026}
}