BGG resolutions via configuration spaces

Michael Falk, Vadim Schechtman, Alexander Varchenko

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)225-245
Number of pages21
JournalJournal de l'Ecole Polytechnique - Mathematiques
Volume1
DOIs
StatePublished - Jan 1 2014

Fingerprint

Configuration Space
Logarithmic
Intersection Cohomology
Flat Connection
Singularity
Form

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

BGG resolutions via configuration spaces. / Falk, Michael; Schechtman, Vadim; Varchenko, Alexander.

In: Journal de l'Ecole Polytechnique - Mathematiques, Vol. 1, 01.01.2014, p. 225-245.

Research output: Contribution to journalArticle

Falk, Michael ; Schechtman, Vadim ; Varchenko, Alexander. / BGG resolutions via configuration spaces. In: Journal de l'Ecole Polytechnique - Mathematiques. 2014 ; Vol. 1. pp. 225-245.
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