Harmonic metrics and connections with irregular singularities
Annales de l'Institut Fourier, Volume 49 (1999) no. 4, p. 1265-1291
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.
Nous identifions le complexe de de Rham de l’extension minimale d’un fibré méromorphe à connexion sur une surface de Riemann compacte X au complexe L 2 associé à ce fibré sur la surface de Riemann privée des pôles, lorsqu’on munit celui-ci d’une métrique convenable et la surface épointée d’une métrique complète. En appliquant des résultats de C. Simpson, nous montrons l’existence d’une métrique harmonique sur ce fibré, donnant lieu au même complexe L 2 .
@article{AIF_1999__49_4_1265_0,
     author = {Sabbah, Claude},
     title = {Harmonic metrics and connections with irregular singularities},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {49},
     number = {4},
     year = {1999},
     pages = {1265-1291},
     doi = {10.5802/aif.1717},
     mrnumber = {2001f:32051},
     zbl = {0947.32019},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_1999__49_4_1265_0}
}
Sabbah, Claude. Harmonic metrics and connections with irregular singularities. Annales de l'Institut Fourier, Volume 49 (1999) no. 4, pp. 1265-1291. doi : 10.5802/aif.1717. https://aif.centre-mersenne.org/item/AIF_1999__49_4_1265_0/

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