发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对Griffiths关于全纯向量丛正曲率埃尔米特度量的猜想，证明无法通过函子性纤维构造从关联线丛O_{PE}(1)的正曲率度量得到该向量丛的正曲率度量，为该猜想的相关研究提供了关键结论。
AI 中文摘要
在紧基上的任意全纯向量丛E都可关联一个记为O_{PE}(1)的线丛。根据Griffiths的猜想，若O_{PE}(1)容许正曲率埃尔米特度量k，则E也容许正曲率埃尔米特度量h。本文证明，尽管该猜想可能成立，但无法通过函子性的纤维构造从k得到h。
英文摘要
With any holomorphic vector bundle $E$ over a compact base one can associate a line bundle, denoted $O_{PE}(1)$. According to a conjecture of Griffiths, if $O_{PE}(1)$ admits a positively curved hermitian metric $k$, then $E$ also admits a positively curved hermitian metric, $h$. In this paper we show that, while the conjecture may be correct, it is not possible to obtain $h$ out of $k$ by a fiberwise construction that is functorial.
CommentsThe abstract already appeared, by mistake, accompanying submission arXiv:2608.22689. The mistake has since been corrected; this abstract here belongs to the current submission
