Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties
arXiv:2510.21677
Abstract
We solve a non-Archimedean Monge-Ampère 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-Ampère 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.
38 pages. Comments very welcome!