Lefschetz decomposition and the cd-index of fans
Algebraic Geometry
2007-05-23 v1 Combinatorics
Abstract
The goal of this article is to give a Lefschetz type decomposition for the cd-index of a complete fan. To a complete simplicial fan one can associate a toric variety X, the even Betti numbers h_i of X and the numbers g_i = h_i-h_{i-1}. If the fan is projective, then non-negativity of g_i follows from the Lefschetz decomposition of the cohomology. In the case of a nonsiplicial complete fan one can analogously compute the flag h-numbers h_S and, by a change of variable formula, the cd-index. We give an analogue of the Lefschetz operation for the cd-index. This gives another proof of the non-negativity of the cd-index for complete fans.
Cite
@article{arxiv.math/0509220,
title = {Lefschetz decomposition and the cd-index of fans},
author = {Kalle Karu},
journal= {arXiv preprint arXiv:math/0509220},
year = {2007}
}
Comments
14 pages, 1 figure