BGG resolutions via configuration spaces

Michael Falk; Vadim Schechtman; Alexander Varchenko

doi:10.5802/jep.9

BGG resolutions via configuration spaces

Michael Falk, Vadim Schechtman, Alexander Varchenko

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 sl₂ Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.

Original language	English (US)
Pages (from-to)	225-245
Number of pages	21
Journal	Journal de l'Ecole Polytechnique - Mathematiques
Volume	1
DOIs	https://doi.org/10.5802/jep.9
State	Published - 2014

Keywords

Aomoto complex
BGG resolution
Cohomology
Configuration space
Local system
Normal-crossing divisor
Orlik-Solomon algebra
Residue
Resolution

ASJC Scopus subject areas

General Mathematics

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10.5802/jep.9

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abstract = "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 sl2 Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.",

keywords = "Aomoto complex, BGG resolution, Cohomology, Configuration space, Local system, Normal-crossing divisor, Orlik-Solomon algebra, Residue, Resolution",

author = "Michael Falk and Vadim Schechtman and Alexander Varchenko",

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AU - Schechtman, Vadim

AU - Varchenko, Alexander

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Y1 - 2014

N2 - 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 sl2 Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.

AB - 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 sl2 Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.

KW - Aomoto complex

KW - BGG resolution

KW - Cohomology

KW - Configuration space

KW - Local system

KW - Normal-crossing divisor

KW - Orlik-Solomon algebra

KW - Residue

KW - Resolution

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JO - Journal de l'Ecole Polytechnique - Mathematiques

JF - Journal de l'Ecole Polytechnique - Mathematiques

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BGG resolutions via configuration spaces

Abstract

Keywords

ASJC Scopus subject areas

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