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arXiv · 2503.22150

Uniform vector bundles over $\mathbb{P}^4$

Rong Du·Yuhang Zhou
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Abstract

There is a long-standing conjecture which states that every uniform algebraic vector bundle of rank $r<2n$ on the $n$-dimensional projective space $\mathbb{P}^n$ over an algebraically closed field of characteristic $0$ is homogeneous. This conjecture is valid for $n\leq3$. In this paper, we classify all uniform vector bundles of rank $r<8$ over $\mathbb{P}^4$ and show that the conjecture holds for $n=4$.

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Rong Du, Yuhang Zhou. 2025-03-28. Uniform vector bundles over $\mathbb{P}^4$. https://arxiv.org/abs/2503.22150

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