BGG resolutions via configuration spaces
Journal de l’École polytechnique — Mathématiques, Volume 1 (2014), pp. 225-245.

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 𝔰𝔩 2 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 𝔰𝔩 2 comme un complexe d’Aomoto.

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Accepted:
Published online:
DOI: 10.5802/jep.9
Classification: 55R80, 17B10, 32S22, 17B55
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

1 Department of Mathematics and Statistics, Northern Arizona University Flagstaff, AZ 86011, USA
2 Institut de Mathématiques de Toulouse, Université Paul Sabatier 118 Route de Narbonne, 31062 Toulouse, France
3 Department of Mathematics, University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3250, USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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