A numerically flat rank-two bundle without a holomorphic connection on a $\partial\bar\partial$-threefold
Year: 2026
Type: preprint
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. This gives, in particular, a negative answer to a question posed by Cao--Deng--Matsumura. In contrast, for compact simply connected complex manifolds $X$, we prove that the answer is affirmative if $H^1(X,\mathcal O_X)=0$, and hence if the Frölicher spectral sequence of $X$ degenerates at $E_1$.
Source: arXiv (Cornell University)
Authors: Hu, Tianzhi, Zhang, Runze
Institution: Wuhan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212002175