BGG resolutions via configuration spaces
[Résolutions BGG via les espaces de configurations]
Falk, Michael ; Schechtman, Vadim ; Varchenko, Alexander
Journal de l'École polytechnique - Mathématiques, Tome 1 (2014), p. 225-245 / Harvested from Numdam
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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.

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.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/jep.9
Classification:  55R80,  17B10,  32S22,  17B55
Mots clés: Espace de configuration, diviseur à croisements normaux, résolution, résidu, système local, cohomologie, algèbre d’Orlik-Solomon, complexe d’Aomoto, résolution BGG 
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     author = {Falk, Michael and Schechtman, Vadim and Varchenko, Alexander},
     title = {BGG resolutions via configuration spaces},
     journal = {Journal de l'\'Ecole polytechnique - Math\'ematiques},
     volume = {1},
     year = {2014},
     pages = {225-245},
     doi = {10.5802/jep.9},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEP_2014__1__225_0}
}

Falk, Michael; Schechtman, Vadim; Varchenko, Alexander. BGG resolutions via configuration spaces. Journal de l'École polytechnique - Mathématiques, Tome 1 (2014) pp. 225-245. doi : 10.5802/jep.9. http://gdmltest.u-ga.fr/item/JEP_2014__1__225_0/

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