Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Lempert, Laszlo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206213201