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arXiv · 2310.09788

Large rank simple bundles of all homological dimensions

Kaiying Hou
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Abstract

For $n\geq 3$ and $r\geq n$, we show that there are rank-$r$ vector bundles on $\mathbb{P}^n$ with arbitrary homological dimension. We apply the Bernstein-Gel'fand-Gel'fand correspondence to translate the vector bundle question into a problem on modules over the exterior algebra. Then, we use linear algebra to construct the desired modules.

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Kaiying Hou. 2023-10-15. Large rank simple bundles of all homological dimensions. https://arxiv.org/abs/2310.09788

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