Infinite-Dimensional Flats in the Space of Positive Metrics on an Ample Line Bundle

Artikel i vetenskaplig tidskrift, 2025

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