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arXiv · 2510.21677

Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties

Ying Wang
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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.

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Ying Wang. 2025-10-24. Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties. https://arxiv.org/abs/2510.21677

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