论文标题
正常品种主束的对数连接
Logarithmic connections on principal bundles over normal varieties
论文作者
论文摘要
让$ x $成为特征零的代数封闭字段的普通投影品种。让$ d $成为$ x $的减少的Weil除数。令$ g $为一个还原线性代数组。我们在$ x $上介绍了对数$ g $ undle的对数连接的概念，该$ x $沿$ d $是单数。如果$ x $的对数切线切型套件本地释放，则在$ x $上与矢量束相关的框架束上存在对数连接的框架捆绑包。此外，当代数组$ g $是半imple时，我们表明校长$ g $ - 邦德尔在且仅当关联的隔壁捆绑包上一个时就承认对数连接。我们还证明，沿边界除数的奇异品种上的主束上的对数连接的存在与捆绑包上的圆环等效结构的存在相当。
Let $X$ be a normal projective variety over an algebraically closed field of characteristic zero. Let $D$ be a reduced Weil divisor on $X$. Let $G$ be a reductive linear algebraic group. We introduce the notion of a logarithmic connection on a principal $G$-bundle over $X$, which is singular along $D$. The existence of a logarithmic connection on the frame bundle associated with a vector bundle over $X$ is shown to be equivalent to the existence of a logarithmic covariant derivative on the vector bundle if the logarithmic tangent sheaf of $X$ is locally free. Additionally, when the algebraic group $G$ is semisimple, we show that a principal $G$-bundle admits a logarithmic connection if and only if the associated adjoint bundle admits one. We also prove that the existence of a logarithmic connection on a principal bundle over a toric variety, singular along the boundary divisor, is equivalent to the existence of a torus equivariant structure on the bundle.
