Remarks on the combinatorial intersection cohomology of fans
| dc.creator | Braden, Tom | |
| dc.date | 2005-11-19 | |
| dc.date | 2006-10-02 | |
| dc.date.accessioned | 2026-07-07T06:51:28Z | |
| dc.date.available | 2026-07-07T06:51:28Z | |
| dc.description | We review the theory of combinatorial intersection cohomology of fans developed by Barthel-Brasselet-Fieseler-Kaup, Bressler-Lunts, and Karu. This theory gives a substitute for the intersection cohomology of toric varieties which has all the expected formal properties but makes sense even for non-rational fans, which do not define a toric variety. As a result, a number of interesting results on the toric $g$ and $h$ polynomials have been extended from rational polytopes to general polytopes. We present explicit complexes computing the combinatorial IH in degrees one and two; the degree two complex gives the rigidity complex previously used by Kalai to study $g_2$. We present several new results which follow from these methods, as well as previously unpublished proofs of Kalai that $g_k(P) = 0$ implies $g_k(P^*) = 0$ and $g_{k+1}(P) = 0$. | |
| dc.description | 34 pages. Typos fixed; final version, to appear in Pure and Applied Math Quarterly | |
| dc.identifier | https://arxiv.org/abs/math/0511488 | |
| dc.identifier | http://arxiv.org/abs/math/0511488 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104999 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.title | Remarks on the combinatorial intersection cohomology of fans | |
| dc.type | text |