Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties
Algebraic Geometry
2025-10-27 v1 Differential Geometry
Abstract
We solve a non-Archimedean Monge-Amp\`ere equation on the Berkovich analytification of a complex log Calabi-Yau pair whose dual complex is a standard simplex, answering a question of Collins-Li and offering a non-Archimedean analog of Ricci-flat metric potentials on complex affine varieties. This work builds on the solution to a complex Monge-Amp\`ere equation obtained by Collins-Li and Collins-Tong-Yau. We also show the suitably rescaled limits of the complex potentials coincide with their non-Archimedean counterparts in some situations, strengthening their connections.
Keywords
Cite
@article{arxiv.2510.21677,
title = {Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties},
author = {Ying Wang},
journal= {arXiv preprint arXiv:2510.21677},
year = {2025}
}
Comments
38 pages. Comments very welcome!