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arXiv · 2609.08757

A numerically flat rank-two bundle without a holomorphic connection on a $\partial\bar\partial$-threefold

Tianzhi Hu·Runze Zhang
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Abstract

We construct a numerically flat holomorphic vector bundle of rank two on a compact complex threefold satisfying the ordinary $\partial\bar\partial$-lemma and prove that it admits no holomorphic connection, thereby giving,in particular, a negative answer to a question posed by Cao--Deng--Matsumura.

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Tianzhi Hu, Runze Zhang. 2026-09-08. A numerically flat rank-two bundle without a holomorphic connection on a $\partial\bar\partial$-threefold. https://arxiv.org/abs/2609.08757

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