Nahm transform and parabolic minimal Laplace transform
Algebraic Geometry
2012-08-06 v2
Abstract
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 -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.
Cite
@article{arxiv.0704.2744,
title = {Nahm transform and parabolic minimal Laplace transform},
author = {Szilard Szabo},
journal= {arXiv preprint arXiv:0704.2744},
year = {2012}
}