We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.
Nous étudions les éclatements d’espaces de configuration. Ces espaces ont une structure de variété que nous appelons d’Orlik-Solomon ; elle permet de calculer la cohomologie d’intersection de certaines connexions plates avec singularités logarithmiques à l’aide de complexes de formes logarithmiques du type d’Aomoto. En utilisant cette construction, nous donnons une réalisation géométrique de la résolution de Bernstein–Gelfand–Gelfand pour comme un complexe d’Aomoto.
Accepted:
Published online:
DOI: 10.5802/jep.9
Keywords: Configuration space, normal-crossing divisor, resolution, residue, local system, cohomology, Orlik-Solomon algebra, Aomoto complex, BGG resolution
Mot clés : Espace de configuration, diviseur à croisements normaux, résolution, résidu, système local, cohomologie, algèbre d’Orlik-Solomon, complexe d’Aomoto, résolution BGG
Michael Falk 1; Vadim Schechtman 2; Alexander Varchenko 3
CC-BY-ND 4.0
@article{JEP_2014__1__225_0,
author = {Michael Falk and Vadim Schechtman and Alexander Varchenko},
title = {BGG resolutions via configuration spaces},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {225--245},
publisher = {\'Ecole polytechnique},
volume = {1},
year = {2014},
doi = {10.5802/jep.9},
mrnumber = {3322788},
zbl = {1323.55013},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.9/}
}
TY - JOUR AU - Michael Falk AU - Vadim Schechtman AU - Alexander Varchenko TI - BGG resolutions via configuration spaces JO - Journal de l’École polytechnique — Mathématiques PY - 2014 SP - 225 EP - 245 VL - 1 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.9/ DO - 10.5802/jep.9 LA - en ID - JEP_2014__1__225_0 ER -
%0 Journal Article %A Michael Falk %A Vadim Schechtman %A Alexander Varchenko %T BGG resolutions via configuration spaces %J Journal de l’École polytechnique — Mathématiques %D 2014 %P 225-245 %V 1 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.9/ %R 10.5802/jep.9 %G en %F JEP_2014__1__225_0
Michael Falk; Vadim Schechtman; Alexander Varchenko. BGG resolutions via configuration spaces. Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 225-245. doi : 10.5802/jep.9. https://jep.centre-mersenne.org/articles/10.5802/jep.9/
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