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A characterization of Griffiths semipositivity by top-degree optimal ∂̅-estimates
Abstract
We prove that a singular Hermitian metric h on a vector bundle agrees almost everywhere with a Griffiths semipositive metric if its dual metric h* is locally integrable and the ∂̅-equation admits solutions with optimal L2-estimates for (n,n)-forms, where n is the dimension of the base manifold. In particular, under this integrability assumption, Nakano semipositivity in the sense of optimal estimates implies Griffiths semipositivity.
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BibTeX
@misc{matsumura2026characterization,
title = {{A characterization of Griffiths semipositivity by top-degree optimal $\bar \partial$-estimates}},
author = {Shin-ichi Matsumura},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25900},
eprint = {2610.25900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25900},
}
RIS
TY - UNPB
TI - A characterization of Griffiths semipositivity by top-degree optimal ∂̅-estimates
AU - Shin-ichi Matsumura
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25900
UR - https://arxiv.org/abs/2610.25900
AB - We prove that a singular Hermitian metric h on a vector bundle agrees almost everywhere with a Griffiths semipositive metric if its dual metric h^* is locally integrable and the ∂̅-equation admits solutions with optimal L^2-estimates for (n,n)-forms, where n is the dimension of the base manifold. In particular, under this integrability assumption, Nakano semipositivity in the sense of optimal estimates implies Griffiths semipositivity.
ER -