Nahm transform and parabolic minimal Laplace transform

Details Nahm transform and parabolic minimal Laplace transform Nahm transform and parabolic minimal Laplace transform

2007-04-20

arxiv.org/abs/0704.2744v2

Mathematics

Algebraic Geometry

Major revision of the exposition, new title, with essentially unmodified results

Scientific paper

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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