Asymptotics of Fubini-Study Currents for Sequences of Line Bundles

Melody Wolff

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arXiv · 2410.09265

Asymptotics of Fubini-Study Currents for Sequences of Line Bundles

Melody Wolff

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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.

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Melody Wolff. 2024-10-11. Asymptotics of Fubini-Study Currents for Sequences of Line Bundles. https://arxiv.org/abs/2410.09265

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