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arXiv · 2609.37309

Stable ample vector bundles without semipositive Kobayashi curvature

Kefeng Liu·Xueyuan Wan
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Abstract

We construct slope-stable ample rank-two vector bundles on every Hirzebruch surface $\mathbb{F}_e$ that admit no smooth strongly pseudoconvex Finsler metric with semipositive Kobayashi curvature. These examples give a negative answer to Kobayashi's problem. The same bundles give counterexamples to the smooth strongly pseudoconvex Finsler formulation of Fulton's problem and to the Hartshorne--Schneider conjecture on the convexity of complements. For $e=1$, these counterexamples have a simply connected Fano base that is not a product.

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Kefeng Liu, Xueyuan Wan. 2026-09-29. Stable ample vector bundles without semipositive Kobayashi curvature. https://arxiv.org/abs/2609.37309

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