Last updates: 17 February 2011
Let $X$ be an algebraic variety over $\u2102$ with the Zariski topology.
$\mathcal{M}=\mathrm{span-}\left\{{\chi}_{A}\phantom{\rule{.5em}{0ex}}\right|\phantom{\rule{.5em}{0ex}}A\phantom{\rule{.5em}{0ex}}\text{is constructible}\}$. | (constfcn) |
$\mathcal{Z}=\mathrm{span-}\left\{\phantom{\rule{.5em}{0ex}}\text{irreducible components}\phantom{\rule{.5em}{0ex}}Z\phantom{\rule{.5em}{0ex}}\text{of}\phantom{\rule{.5em}{0ex}}X\right\}$ |
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.