Nahm变换与抛物型极小拉普拉斯变换
Nahm transform and parabolic minimal Laplace transform
摘要：
我们证明了Nahm变换的可积连接与有限数量的正则奇点和一个不规则的奇异秩1的黎曼球面上是等价的-考虑可积连接作为完整的$\D$ -模块-最小的拉普拉斯变换。我们假设半简单性和共振自由度条件，我们的工作框架中的对象具有抛物结构。特别地，我们描述了由于C.萨巴主要结果的证明依赖于对扭曲的de Rham复形的研究。
英文摘要：
We prove that Nahm transform for integrable connections with a finite number of regular singularities and an irregular singularity of rank 1 on the Riemann sphere is equivalent -- up to considering integrable connections as holonomic $\D$-modules -- to minimal Laplace transform. We assume semi-simplicity and resonance-freeness conditions, and we work in the framework of objects with a parabolic structure. In particular, we describe the definition of the parabolic version of Laplace transform due to C. Sabbah. The proof of the main result relies on the study of a twisted de Rham complex.
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