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Griffiths positivity does not imply positivity of the top Chern form
Abstract
For every integer rβ₯9, we construct a smooth Griffiths-positive Hermitian metric on πͺβr(1)β r whose top Chern form is pointwise negative on a nonempty open set. This gives counterexamples on compact projective manifolds to Griffiths' conjecture on the positivity of Chern--Weil forms.
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BibTeX
@misc{du2026griffiths,
title = {{Griffiths positivity does not imply positivity of the top Chern form}},
author = {Yun-Heng Du},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05931},
eprint = {2610.05931},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05931},
}
RIS
TY - UNPB
TI - Griffiths positivity does not imply positivity of the top Chern form
AU - Yun-Heng Du
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05931
UR - https://arxiv.org/abs/2610.05931
AB - For every integer rβ₯9, we construct a smooth Griffiths-positive Hermitian metric on πͺ_β^r(1)^β r whose top Chern form is pointwise negative on a nonempty open set. This gives counterexamples on compact projective manifolds to Griffiths' conjecture on the positivity of Chern--Weil forms.
ER -