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On polarizations of affine Calabi--Yau varieties
Abstract
Let $(X, Ω)$ be an affine Calabi--Yau variety, by which we mean a klt affine variety X with a non-vanishing algebraic volume form Ω. In connection with complete Calabi--Yau metrics of Euclidean volume growth on $(X, Ω)$, we study algebraic aspects of polarizations of X given by a negative valuation. We show that such a valuation is finitely generated with a klt degeneration if and only if X admits a dlt log Fano type compactification, generalizing a compactification considered by Tian--Yau. We further give a valuative criterion detecting K-semistability of the degeneration by a negative valuation.
Related
- Special valuations and automorphisms of affine log Calabi--Yau varieties
- On the Witt liftability of quasi-F-split Calabi--Yau varieties
- Characterising canonical lifts of ordinary Calabi-Yau varieties
- Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties
- Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces
BibTeX
@misc{wu2026polarizations,
title = {{On polarizations of affine Calabi--Yau varieties}},
author = {Yueqiao Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32036},
eprint = {2610.32036},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32036},
}
RIS
TY - UNPB
TI - On polarizations of affine Calabi--Yau varieties
AU - Yueqiao Wu
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32036
UR - https://arxiv.org/abs/2610.32036
AB - Let $(X, Ω)$ be an affine Calabi--Yau variety, by which we mean a klt affine variety X with a non-vanishing algebraic volume form Ω. In connection with complete Calabi--Yau metrics of Euclidean volume growth on $(X, Ω)$, we study algebraic aspects of polarizations of X given by a negative valuation. We show that such a valuation is finitely generated with a klt degeneration if and only if X admits a dlt log Fano type compactification, generalizing a compactification considered by Tian--Yau. We further give a valuative criterion detecting K-semistability of the degeneration by a negative valuation.
ER -