论文标题
$ \ mathbb {p}^{5} $在$ \ mathbb上的特殊通用零相关捆绑包的稳定性
Stability of special generalized null correlation bundles on $\mathbb{P}^{5}$
论文作者
论文摘要
在本文中，我们在$ \ mathbb {p}^{5} $上研究特殊的广义零相关捆绑包。我们证明，在某些数值条件下，$ \ mathbb {p}^{5} $上的特殊通用零相关捆绑包是稳定的。此外，我们证明，稳定的特殊通用零相关束的亚各种参数化的封闭是模量空间$ 4 $ 4 $稳定矢量捆绑包的不可约组件，并在$ \ mathbb {p}^{5} $上具有相应的Chern类别。作为一个应用程序，我们证明，$ 4 $ 4 $稳定的向量捆绑包在$ \ mathbb {p}^5 $上，带有一些固定的切尔恩类的不可约组件的数量可以任意高。
In this paper, we study special generalized null correlation bundles on $\mathbb{P}^{5}$. We prove that special generalized null correlation bundles on $\mathbb{P}^{5}$ are stable under some numerical conditions. Moreover, we prove that the closure of the subvariety parametrizing stable special generalized null correlation bundles is an irreducible component of the moduli space of rank $4$ stable vector bundles with corresponding Chern classes on $\mathbb{P}^{5}$. As an application, we prove that the number of irreducible components of moduli space of rank $4$ stable vector bundles on $\mathbb{P}^5$ with some fixed Chern classes can be arbitrarily high.
