Harmonic metrics and connections with irregular singularities

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

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Algebraic Geometry, 32S40, 32S60, 32L10, 35A20, 35A27

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http://salesiana.dossiersoluciones.com/handle/123456789/78465

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9905039
 http://arxiv.org/abs/math/9905039
 Ann. Institut Fourier (Grenoble) 49 (1999), p. 1265-1291

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arXiv