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A first-jet characterization of Griffiths positivity
Abstract
We characterize Griffiths positivity of vector bundles on smooth projective varieties by a finite-dimensional convex condition on first jets of sections of positive twists. A nonzero positive matrix-valued measure annihilated by the adjoint Levi operator gives the dual obstruction. We also give an explicit bundle on an abelian surface that satisfies the first-level condition, but whose complete untwisted evaluation has a differential kernel.
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BibTeX
@misc{du2026firstjet,
title = {{A first-jet characterization of Griffiths positivity}},
author = {Yun-Heng Du and Song-Yan Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26528},
eprint = {2609.26528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26528},
}
RIS
TY - UNPB
TI - A first-jet characterization of Griffiths positivity
AU - Yun-Heng Du
AU - Song-Yan Xie
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26528
UR - https://arxiv.org/abs/2609.26528
AB - We characterize Griffiths positivity of vector bundles on smooth projective varieties by a finite-dimensional convex condition on first jets of sections of positive twists. A nonzero positive matrix-valued measure annihilated by the adjoint Levi operator gives the dual obstruction. We also give an explicit bundle on an abelian surface that satisfies the first-level condition, but whose complete untwisted evaluation has a differential kernel.
ER -