Harmonic metrics and connections with irregular singularities

Details Harmonic metrics and connections with irregular singularities Harmonic metrics and connections with irregular singularities

1999-05-06

arxiv.org/abs/math/9905039v1

Ann. Institut Fourier (Grenoble) 49 (1999), p. 1265-1291

Mathematics

Algebraic Geometry

AMS-LaTeX with XyPic macro package. 20 pages. To appear in Ann. Institut Fourier (Grenoble) vol. 49 (1999)

Scientific paper

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L^2 complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same L^2 complex. As a consequence, we obtain a Hard Lefschetz-type theorem.

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