Symmetric polynomials and divided differences in formulas of intersection theory
| dc.creator | Pragacz, Piotr | |
| dc.date | 1996-05-28 | |
| dc.date.accessioned | 2026-07-07T09:06:49Z | |
| dc.date.available | 2026-07-07T09:06:49Z | |
| dc.description | The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci; some explicit formulas for the Chern and Segre classes of Schur bundles with applications to enumerative geometry; flag degeneracy loci; fundamental classes, diagonals and Gysin maps; intersection rings of G/P and formulas for isotropic degeneracy loci; numerically positive polynomials for ample vector bundles. Apart of surveyed results, the paper contains also some new results as well as some new proofs of earlier ones: how to compute the fundamental class of a subvariety from the class of the diagonal of the ambient space; how to compute the class of the relative diagonal using Gysin maps; a new formula for pushing forward Schur's Q- polynomials in Grassmannian bundles; a new formula for the total Chern class of a Schur bundle; another proof of Schubert's and Giambelli's enumeration of complete quadrics; an operator proof of the Jacobi-Trudi formula; a Schur complex proof of the Giambelli-Thom-Porteous formula. | |
| dc.description | 58 pages; to appear in the volume "Parameter Spaces", Banach Center Publications vol 36 (1996) AMSTEX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9605014 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9605014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150152 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Primary: 14C15, 14C25, 14M15, 14N10, 57R20 05E05; Secondary: 14M12, 14H40, 14J60, 32S20, 55R40, 05E15 | |
| dc.title | Symmetric polynomials and divided differences in formulas of intersection theory | |
| dc.type | text |