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arXiv · 2609.26504

Ample vector bundles without Griffiths-semipositive metrics

Yun-Heng Du·Song-Yan Xie
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Abstract

We construct a rank-two ample holomorphic vector bundle on an abelian surface that admits no smooth Griffiths-semipositive Hermitian metric, thereby giving a counterexample to the Griffiths conjecture. The proof combines a curvature obstruction that persists under deformations with the openness of ampleness in an irreducible moduli space of stable sheaves.

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Yun-Heng Du, Song-Yan Xie. 2026-09-22. Ample vector bundles without Griffiths-semipositive metrics. https://arxiv.org/abs/2609.26504

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