Year: 2025
Type: article
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 $\mathcal{F}$ of the section ring of $L$, the set of bounded decreasing convex functions on the support of the Duistermaat–Heckman measure of $\mathcal{F}$ 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 ($p=2$).
DOI: 10.1093/imrn/rnaf342
Authors: Rémi Reboulet, David Witt Nyström
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416268767