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arXiv · 2311.13451

Infinite-dimensional flats in the space of positive metrics on an ample line bundle

Rémi Reboulet·David Witt Nyström
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Abstract

We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded filtration F of the section ring of L, the set of bounded decreasing convex functions on the support of the Duistermaat--Heckman measure of F embeds L^p-isometrically into the space of bounded positive metrics on L with respect to Darvas' d_p distance for all p\in[1,\infty), and in particular with respect to the Mabuchi metric (p=2).

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Rémi Reboulet, David Witt Nyström. 2025-10-29. Infinite-dimensional flats in the space of positive metrics on an ample line bundle. https://arxiv.org/abs/2311.13451

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