English

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}
}