SAGBI bases and Degeneration of Spherical Varieties to Toric Varieties
| dc.creator | Kaveh, Kiumars | |
| dc.date | 2003-09-25 | |
| dc.date.accessioned | 2026-07-07T05:01:26Z | |
| dc.date.available | 2026-07-07T05:01:26Z | |
| dc.description | Let X \subset Proj(V) be a projective spherical G-variety, where V is a finite dimensional G-module and G = SP(2n, C). In this paper, we show that X can be deformed, by a flat deformation, to the toric variety corresponding to a convex polytope Δ(X). The polytope Δ(X) is the polytope fibred over the moment polytope of X with the Gelfand-Cetlin polytopes as fibres. We prove this by showing that if X is a horospherical variety, e.g. flag varieties and Grassmanians, the homogeneous coordinate ring of X can be embedded in a Laurent polynomial algebra and has a SAGBI basis with respect to a natural term order. Moreover, we show that the semi-group of initial terms, after a linear change of variables, is the semi-group of integral points in the cone over the polytope Δ(X). The results of this paper are true for other classical groups, provided that a result of A. Okounkov on the representation theory of SP(2n,C) is shown to hold for other classical groups. | |
| dc.description | 17 pages, LaTex, uses the package xy | |
| dc.identifier | https://arxiv.org/abs/math/0309413 | |
| dc.identifier | http://arxiv.org/abs/math/0309413 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68670 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14M17; 13P10 | |
| dc.title | SAGBI bases and Degeneration of Spherical Varieties to Toric Varieties | |
| dc.type | text |