论文标题
福利主束的分类，降低和稳定性
Classification, reduction and stability of toric principal bundles
论文作者
论文摘要
让$ x $成为一个复杂的感谢您，配备了代数圆环$ t $的作用，让$ g $是一个复杂的线性代数组。我们将所有$ t $ equivariant principal $ g $ g $ bundles $ \ mathcal {e} $上的$ x $及其之间的摩相和形态进行分类。当$ g $连接和还原时，我们将$ \ text {aut} _t（\ Mathcal {e}）$ $ \ Mathcal {e} $表征为$ t $ t $ t $ t $ tho $ nmats $ n Math的$ g $的相交。然后，我们将$ \ MATHCAL {E} $的结构组减少到$ \ text {aut} _t（\ Mathcal {e}）$方面的结构组的标准。我们用它来证明Kaneyama定理的主要捆绑包模拟于在投影空间上的小级别的圆环矢量捆绑包。当$ x $是投射的，并且$ g $连接并还原时，我们表明，对于任何$ t $ equivariant principal $ g $ g $ bundle均超过$ x $，稳定性和均衡稳定性的概念是等效的。
Let $X$ be a complex toric variety equipped with the action of an algebraic torus $T$, and let $G$ be a complex linear algebraic group. We classify all $T$-equivariant principal $G$-bundles $\mathcal{E}$ over $X$ and the morphisms between them. When $G$ is connected and reductive, we characterize the equivariant automorphism group $\text{Aut}_T(\mathcal{E} )$ of $\mathcal{E}$ as the intersection of certain parabolic subgroups of $G$ that arise naturally from the $T$-action on $\mathcal{E}$. We then give a criterion for the equivariant reduction of the structure group of $\mathcal{E}$ to a Levi subgroup of $G$ in terms of $\text{Aut}_T(\mathcal{E} )$. We use it to prove a principal bundle analogue of Kaneyama's theorem on equivariant splitting of torus equivariant vector bundles of small rank over a projective space. When $X$ is projective and $G$ is connected and reductive, we show that the notions of stability and equivariant stability are equivalent for any $T$-equivariant principal $G$-bundle over $X$.
