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arXiv · 2609.26528

A first-jet characterization of Griffiths positivity

Yun-Heng Du·Song-Yan Xie
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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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Yun-Heng Du, Song-Yan Xie. 2026-09-22. A first-jet characterization of Griffiths positivity. https://arxiv.org/abs/2609.26528

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