PreprintCC BY-NC-ND 4.0arXiv
On a construction of hermitian metrics on holomorphic vector bundles
Abstract
With any holomorphic vector bundle E over a compact base one can associate a line bundle, denoted OPE(1). According to a conjecture of Griffiths, if OPE(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.
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BibTeX
@misc{lempert2026construction,
title = {{On a construction of hermitian metrics on holomorphic vector bundles}},
author = {Laszlo Lempert},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00326},
eprint = {2609.00326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00326},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On a construction of hermitian metrics on holomorphic vector bundles
AU - Laszlo Lempert
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00326
UR - https://arxiv.org/abs/2609.00326
AB - 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.
ER -