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arXiv · 2212.01360

Ueda's lemma via uniform Hörmander estimates for flat line bundles

Yoshinori Hashimoto·Takayuki Koike
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Abstract

We establish Hörmander-type $L^2$-estimates for the $\overline{\partial}$-operators that hold uniformly for all nontrivial flat holomorphic line bundles on compact Kähler manifolds. Our result can be regarded as a $\overline{\partial}$-version of Ueda's lemma on the operator norm of Čech coboundaries for flat line bundles and indeed recovers the original version of Ueda's lemma for compact Kähler manifolds. A partial generalisation for $(p,0)$-forms on Ricci-flat manifolds is also given.

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Yoshinori Hashimoto, Takayuki Koike. 2023-04-03. Ueda's lemma via uniform Hörmander estimates for flat line bundles. https://arxiv.org/abs/2212.01360

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