Mathematische Annalen

, Volume 321, Issue 3, pp 533–551

From moment graphs to intersection cohomology


  • Tom Braden
    • Harvard University, Department of Mathematics, Cambridge, MA 02138, USA (e-mail:
  • Robert MacPherson
    • Princeton University, School of Mathematics, Institute for Advanced Study Princeton, NJ 08540, USA (e-mail:

DOI: 10.1007/s002080100232

Cite this article as:
Braden, T. & MacPherson, R. Math Ann (2001) 321: 533. doi:10.1007/s002080100232


We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our formula applies includes Schubert varieties in flag varieties and affine flag varieties. We also prove a monotonicity result on local intersection cohomology stalks.

Mathematics Subject Classification (1991): 32S60, 14M15, 58K70
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© Springer-Verlag Berlin Heidelberg 2001