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arXiv · 2409.05300

Uniform $L^2$-estimates for flat nontrivial line bundles on compact complex manifolds

Yoshinori Hashimoto·Takayuki Koike·Shin-ichi Matsumura
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Abstract

In this paper, we extend the uniform $L^2$-estimate of $\bar{\partial}$-equations for flat nontrivial line bundles, proved for compact K\"ahler manifolds in the previous work, to compact complex manifolds. In the proof, by tracing the Dolbeault isomorphism in detail, we derive the desired $L^2$-estimate directly from Ueda's lemma.

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Yoshinori Hashimoto, Takayuki Koike, Shin-ichi Matsumura. 2024-09-09. Uniform $L^2$-estimates for flat nontrivial line bundles on compact complex manifolds. https://arxiv.org/abs/2409.05300

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