On orbit closures of Borel subgroups in spherical varieties
| dc.creator | Brion, Michel | |
| dc.date | 1999-08-18 | |
| dc.date | 1999-11-12 | |
| dc.date.accessioned | 2026-07-07T05:30:23Z | |
| dc.date.available | 2026-07-07T05:30:23Z | |
| dc.description | Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert classes defines a union V_0 of Schubert varieties in F with positive multiplicities. If G is simply-laced, we show that these multiplicites are equal to the same power of 2. For arbitrary G, we show that V_0 is connected in codimension 1. If moreover all multiplicities are 1, we show that the singularities of V are rational, and we construct a flat degeneration of V to V_0. Thus, for any effective line bundle L on F, the restriction map from H^0(G/B,L) to H^0(V,L) is surjective, and H^i(V,L)=0 for i>0. | |
| dc.description | LaTeX2e, 37 pages, 5 figures; main theorem strengthened, new results added | |
| dc.identifier | https://arxiv.org/abs/math/9908094 | |
| dc.identifier | http://arxiv.org/abs/math/9908094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78974 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14L30; 14M15; 14M17; 20G05 | |
| dc.title | On orbit closures of Borel subgroups in spherical varieties | |
| dc.type | text |