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

Journal article, 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 ().