一个在$\partial\bar\partial$-三维流形上没有全纯联络的数值平坦秩二向量丛
A numerically flat rank-two bundle without a holomorphic connection on a $\partial\bar\partial$-threefold
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中文总结 AI 辅助
在满足$\partial\bar\partial$-引理的紧致复三维流形上构造秩二数值平坦全纯向量丛，证明其无全纯联络，否定回答了Cao--Deng--Matsumura的问题。
中文摘要 AI 辅助
我们在一个满足通常$\partial\bar\partial$-引理的紧致复三维流形上构造了一个秩二的数值平坦全纯向量丛，并证明它不承认任何全纯联络，从而特别地对Cao--Deng--Matsumura提出的一个问题给出了否定回答。
英文摘要
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 $E_1$.
发表机构
- School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
- The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong（香港中文大学数学科学研究所和数学系）
机构由 AI 辅助整理，请以论文原文为准。
