论文标题
对数平面连接的正常形式和模量堆栈
Normal forms and moduli stacks for logarithmic flat connections
论文作者
论文摘要
我们在复杂的歧管上建立了一类奇异平坦连接的正常形式定理，包括沿加权均匀的saito noto noto saito nife saito的连接。结果，我们表明这种连接的模量空间接收了代数商堆栈的结构。为了证明这些结果，我们介绍了同质的lie群体，并研究了他们的表示理论。在这个方向上，我们证明了两个主要结果：Jordan-Chevalley分解定理和一个线性化定理。我们给出明确的正常形式，以提供几个自由分隔的例子，例如均匀的平面曲线，还原的自由除数和Sekiguchi的自由除数之一。
We establish normal form theorems for a large class of singular flat connections on complex manifolds, including connections with logarithmic poles along weighted homogeneous Saito free divisors. As a result, we show that the moduli spaces of such connections admit the structure of algebraic quotient stacks. In order to prove these results, we introduce homogeneous Lie groupoids and study their representation theory. In this direction, we prove two main results: a Jordan-Chevalley decomposition theorem, and a linearization theorem. We give explicit normal forms for several examples of free divisors, such as homogeneous plane curves, reductive free divisors, and one of Sekiguchi's free divisors.
