Last updates: 17 February 2011
Let be an algebraic variety over with the Zariski
A locally closed subset is the intersection of an open set and a closed set.
A constructible subset is a subset
which is a finite union of locally closed subsets.
The vector space of constructible functions
is the span of the characteristic functions of constructible subsets of ,
by requiring that
is equal to 1 on a dense open subset of
and equal to 0 on a dense open subset of any other irreducible
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].
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,