Harmonic metrics and connections with irregular singularities
代数几何
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/9905039,
title = {Harmonic metrics and connections with irregular singularities},
author = {Claude Sabbah},
journal= {arXiv preprint arXiv:math/9905039},
year = {2007}
}
备注
AMS-LaTeX with XyPic macro package. 20 pages. To appear in Ann. Institut Fourier (Grenoble) vol. 49 (1999)