Asymptotics of Fubini-Study Currents for Sequences of Line Bundles
Complex Variables
2024-10-15 v1 Differential Geometry
Abstract
We study the Fubini-Study currents and equilibrium metrics of continuous Hermitian metrics on sequences of holomorphic line bundles over a fixed compact K\"ahler manifold. We show that the difference between the Fubini-Study currents and the curvature of the equilibrium metric, when appropriately scaled, converges to 0 in the sense of currents. As a consequence, we obtain sufficient conditions for the scaled Fubini-Study currents to converge weakly.
Keywords
Cite
@article{arxiv.2410.09265,
title = {Asymptotics of Fubini-Study Currents for Sequences of Line Bundles},
author = {Melody Wolff},
journal= {arXiv preprint arXiv:2410.09265},
year = {2024}
}