论文标题
复杂流形的无限性捆绑
Infinitesimally Equivariant Bundles on Complex Manifolds
论文作者
论文摘要
我们表明，任何连续的$ \ mathbf {c} $ - 线性谎言谎言谎言分解符号映射从复杂的歧管上的矢量束的Atiyah代数分裂，这是由订单的不同订单的差分运算符给出的，最多是捆绑包的等级。配备了这种分裂的捆绑包可以被认为是\ emph {imph {无限等等的}捆绑包，我们的定理意味着在某种意义上，在某种意义上是与矢量捆绑包具有平坦连接的正式正式社区。
We show that any continuous $\mathbf{C}$-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator of order at most the rank of the bundle plus one. Bundles equipped with such a splitting can be thought of as \emph{infinitesimally equivariant} bundles, and our theorem implies these are, in a certain sense, in a categorical formal neighbourhood of vector bundles with a flat connection.
