论文标题
全球生成的向量捆绑包，$ c_1 = 5 $ on $ \ mathbb {p}^n $，$ n \ geq 4 $
Globally generated vector bundles with $c_1 = 5$ on $\mathbb{P}^n$, $n \geq 4$
论文作者
论文摘要
我们通过治疗$ \ \ \ \ \ \ \ m \ m c_1 = 5 $的情况来完成全球生成的矢量捆绑包，并在投影空间上与小$ c_1 $完成分类。 $ \ mathbb {p}^2 $和$ \ mathbb {p}^3 $已在我们以前的两篇论文中进行了研究）。事实证明，这种不可混合的捆绑包很少：除了一些明显的例子外，粗略地说，只有（第一个转折）等级5矢量捆绑包，这是单月的中期，定义了$ \ mathbb {p}^5 $ of $ \ m arock buns of Cark 3的中等学期，并将其限制为$ \ althbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb^p}^4 $。我们在附录中回想起我们的预印刷[Arxiv：1805.11336]，主要结果允许将$ c_1 = 5 $在$ \ Mathbb {p}^3 $上分类为全球生成的向量束。由于有许多这样的捆绑包，因此纸张主体的很大一部分被占据的事实证明，除了最简单的纸条外，它们不会扩展到$ \ mathbb {p}^4 $，即全球生成的向量捆绑包。
We complete the classification of globally generated vector bundles with small $c_1$ on projective spaces by treating the case $c_1 = 5$ on $\mathbb{P}^n$, $n \geq 4$ (the case $c_1 \leq 3$ has been considered by Sierra and Ugaglia, while the cases $c_1 = 4$ on any projective space and $c_1 = 5$ on $\mathbb{P}^2$ and $\mathbb{P}^3$ have been studied in two of our previous papers). It turns out that there are very few indecomposable bundles of this kind: besides some obvious examples there are, roughly speaking, only the (first twist of the) rank 5 vector bundle which is the middle term of the monad defining the Horrocks bundle of rank 3 on $\mathbb{P}^5$, and its restriction to $\mathbb{P}^4$. We recall, in an appendix, from our preprint [arXiv:1805.11336], the main results allowing the classification of globally generated vector bundles with $c_1 = 5$ on $\mathbb{P}^3$. Since there are many such bundles, a large part of the main body of the paper is occupied with the proof of the fact that, except for the simplest ones, they do not extend to $\mathbb{P}^4$ as globally generated vector bundles.
