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arXiv · 2212.02486

Critical Fubini-Study metrics over non-archimedean fields

Yanbo Fang
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Abstract

Over a non-archimedean local place, the height of a projective variety with respect to a very ample line bundle equipped with a Fubini-Study metric is related to the naive height of its Chow form. Using a non-Archimedean Kempf-Ness criteria, we characterize Fubini-Study metrics that minimize the height under the special linear action in terms of their Monge-Ampère polytopes. This polytope can be constructed either as its non-Archimedean Bergman functional or as the weight polytope for the residual action on its Chow form; it is associated with a polymatroid.

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Yanbo Fang. 2022-12-05. Critical Fubini-Study metrics over non-archimedean fields. https://arxiv.org/abs/2212.02486

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