Constructible functions

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia

Last updates: 17 February 2011

Constructible functions

Let X be an algebraic variety over with the Zariski topology.

𝒵 = span-{ irreducible components Zof X}
and define fZ by requiring that fZ is equal to 1 on a dense open subset of Z and equal to 0 on a dense open subset of any other irreducible component Z.

Notes and References

This summary of the theory of constructible functions is part of joint work with A. Ghitza and S. Kannan on the relationship between MV-cycles and the Borel-Weil-Bott theorem. This presentation follows [GLS, Section 4.1].


[GLS] C. Geiss, B. Leclerc and J. Schröer, Semicanonical bases and preprojective algebras, Ann. Sc. École Norm. Sup. 38 (2005), 193-253. (2003), 567-588, arXiv:math/0402448, MR2144987.

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