Nonexistence of exceptional bundles on $\mathbb{P}^{3}$ with maximal possible ranks

Yeqin Liu

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arXiv · 2302.11743

Nonexistence of exceptional bundles on $\mathbb{P}^{3}$ with maximal possible ranks

Yeqin Liu

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Abstract

We prove that on $\mathbb{P}^{3}$ there is no exceptional bundle with rank $r=2d^{2}+1$ and degree $d$ for every $|d|\geq 4$. In particular, we find a new obstruction for the existence of exceptional bundles other than $r|(2d^{2}+1)$. We also show that there is no exceptional bundle with rank $27$ and degree $11$ to exhibit another different obstruction.

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Yeqin Liu. 2023-02-23. Nonexistence of exceptional bundles on $\mathbb{P}^{3}$ with maximal possible ranks. https://arxiv.org/abs/2302.11743

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