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Cohomology of Real Diagonal Subspace Arrangements via Resolutions

Published online by Cambridge University Press:  04 December 2007

IRENA PEEVA ,
VIC REINER  and
VOLKMAR WELKER
IRENA PEEVA
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; e-mail: irena@math.mit.edu
VIC REINER
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA; e-mail: reiner@math.umn.edu
VOLKMAR WELKER
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; e-mail: irena@math.mit.edu
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Abstract

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We express the cohomology of the complement of a real subspace arrangement of diagonal linear subspaces in terms of the Betti numbers of a minimal free resolution. This leads to formulas for the cohomology in some cases, and also to a cohomology vanishing theorem valid for all arrangements.

Keywords

syzygiessubspace arrangements.
Type
Research Article
Information
Compositio Mathematica , Volume 117 , Issue 1 , May 1999 , pp. 107 - 123
Copyright
© 1999 Kluwer Academic Publishers