Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere

Details Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere

2004-08-22

arxiv.org/abs/math/0408294v2

Russian Math. Surveys 59 (2004), no. 6, 1165--1180 & Mosc. Math. J. 9 (2009), no. 4, 885--898

Mathematics

Algebraic Geometry

13+11 pages, AMSlatex. Original version followed by an Erratum added may 2007 after publication

Scientific paper

We show that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, when one only considers the part at finite distance, a polarizable regular twistor $\mathcal{D}$-module. The associated holomorphic bundle out of the origin is therefore equipped with a natural harmonic metric with a tame behaviour near the origin.

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