On Monge-Amp\`ere volumes of direct images
Differential Geometry
2026-03-25 v2 Spectral Theory
Abstract
This paper is devoted to the study of the asymptotics of Monge-Amp\`ere volumes of direct images associated with high tensor powers of an ample line bundle. We study the leading term of this asymptotics and provide a classification of bundles saturating the topological bound of Demailly. In the special case of high symmetric powers of ample vector bundles, this provides a characterization of vector bundles admitting projectively flat Hermitian structures.
Keywords
Cite
@article{arxiv.2010.01839,
title = {On Monge-Amp\`ere volumes of direct images},
author = {Siarhei Finski},
journal= {arXiv preprint arXiv:2010.01839},
year = {2026}
}