Harmonic metrics and connections with irregular singularities

Claude Sabbah

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 4, page 1265-1291
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Sabbah, Claude. "Harmonic metrics and connections with irregular singularities." Annales de l'institut Fourier 49.4 (1999): 1265-1291. <http://eudml.org/doc/75381>.

@article{Sabbah1999,
abstract = {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.},
author = {Sabbah, Claude},
journal = {Annales de l'institut Fourier},
keywords = {harmonic metric; irregular singularity; meromorphic connection; Poincaré lemma},
language = {eng},
number = {4},
pages = {1265-1291},
publisher = {Association des Annales de l'Institut Fourier},
title = {Harmonic metrics and connections with irregular singularities},
url = {http://eudml.org/doc/75381},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Sabbah, Claude
TI - Harmonic metrics and connections with irregular singularities
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 4
SP - 1265
EP - 1291
AB - 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.
LA - eng
KW - harmonic metric; irregular singularity; meromorphic connection; Poincaré lemma
UR - http://eudml.org/doc/75381
ER -

References

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  10. [10] C. SIMPSON, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc., 1 (1988), 867-918. Zbl0669.58008MR90e:58026
  11. [11] C. SIMPSON, "Harmonic bundles on noncompact curves", J. Amer. Math. Soc., 3 (1990), 713-770. Zbl0713.58012MR91h:58029
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