Schubert induction
| dc.creator | Vakil, Ravi | |
| dc.date | 2003-02-25 | |
| dc.date | 2003-09-26 | |
| dc.date.accessioned | 2026-07-07T04:55:33Z | |
| dc.date.available | 2026-07-07T04:55:33Z | |
| dc.description | We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule, described in a companion paper. Schubert problems are among the most classical problems in enumerative geometry of continuing interest. As an application of Schubert induction, we address several long-standing natural questions related to Schubert problems, including: the "reality" of solutions; effective numerical methods; solutions over algebraically closed fields of positive characteristic; solutions over finite fields; a generic smoothness (Kleiman-Bertini) theorem; and monodromy groups of Schubert problems. These methods conjecturally extend to the flag variety. | |
| dc.description | 22 pages, 13 figures; v2 with new application: surprising examples where the Galois/monodromy group is small, inspired by H. Derksen. The groups are computed using Schubert induction | |
| dc.identifier | https://arxiv.org/abs/math/0302296 | |
| dc.identifier | http://arxiv.org/abs/math/0302296 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66614 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary 14M15, 14N15; Secondary 14N10, 14C17, 14P99, 14Q10, 14G15, 14G27 | |
| dc.title | Schubert induction | |
| dc.type | text |