Atiyah代数胚的表示与对数联络
Representations of Atiyah algebroids and logarithmic connections
摘要：
本文研究复流形$Y$上全纯线丛$N$的Atiyah代数胚$\operatorname{At}(N)$的表示.特别地，我们通过两个函子将$\operatorname{At}(N)$ -模与对数连接联系起来。一方面，我们使用这些函子来定义Atiyah代数胚表示的不变量（monodromy）。另一方面，这为利用李代数胚理论研究对数联络问题开辟了道路;我们将给出这样一个例子，表明对于正则平坦亚纯联络，Deligne扩张的存在性和Riemann-Hilbert对应可以作为$\operatorname{At}(N)$ -模的类似结果的拉回而得到，并且，在这个水平上，这些结果是李第二定理的直接结果。
英文摘要：
In this paper, we investigate representations of $\operatorname{At}(N)$, the Atiyah algebroids of a holomorphic line bundles $N$ over a complex manifold $Y$. In particular, we relate $\operatorname{At}(N)$-modules with logarithmic connections through two functors. On the one hand, we use these functors to the define invariants (monodromy) for representations of Atiyah algebroids. On the other hand, this opens the way to use the theory of Lie algebroids to study problems about logarithmic connections; we will give an example of this by showing that the existence of Deligne's extensions of flat connections and the Riemann-Hilbert correspondence for regular flat meromorphic connections may be obtained as pull-back of similar results for $\operatorname{At}(N)$-modules, and, at this level, these results are a direct consequence of the second theorem of Lie.
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