The Bott Formula for Toric Varieties
| dc.creator | Materov, Evgeny | |
| dc.date | 1999-04-21 | |
| dc.date | 2001-05-14 | |
| dc.date.accessioned | 2026-07-07T05:28:45Z | |
| dc.date.available | 2026-07-07T05:28:45Z | |
| dc.description | The purpose of this paper is to give an explicit formula which allows one to compute the dimension of the cohomology groups of the sheaf $Ω_¶^p(D)$ of p-th differential forms of Zariski twisted by an ample invertible sheaf on a complete simplicial toric variety. The formula involves some combinatorial sums of integer points over all faces of the support polytope for ${Ø_X}(D)$. We also introduce a new combinatorial object, the so-called p-th Hilbert-Erhart polynomial, which generalizes the usual notion and behaves similar. Namely, there exists a generalization of the inversion law for a usual Hilbert-Erhart polynomial. Some applications of the Bott formula are discussed. | |
| dc.description | 18 pages, LaTeX 2e, no figures. Revised version | |
| dc.identifier | https://arxiv.org/abs/math/9904110 | |
| dc.identifier | http://arxiv.org/abs/math/9904110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78382 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M25, 32L10, 58A10 | |
| dc.title | The Bott Formula for Toric Varieties | |
| dc.type | text |