Asymptotics of Fubini-Study Currents for Sequences of Line Bundles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913543195983872 |
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| author | Wolff, Melody |
| author_facet | Wolff, Melody |
| contents | We study the Fubini-Study currents and equilibrium metrics of continuous Hermitian metrics on sequences of holomorphic line bundles over a fixed compact Kähler 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics of Fubini-Study Currents for Sequences of Line Bundles Wolff, Melody Complex Variables Differential Geometry We study the Fubini-Study currents and equilibrium metrics of continuous Hermitian metrics on sequences of holomorphic line bundles over a fixed compact Kähler 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. |
| title | Asymptotics of Fubini-Study Currents for Sequences of Line Bundles |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2410.09265 |