2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150152The 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.58 pages; to appear in the volume "Parameter Spaces", Banach Center Publications vol 36 (1996) AMSTEXAlgebraic GeometryPrimary: 14C15, 14C25, 14M15, 14N10, 57R20 05E05; Secondary: 14M12, 14H40, 14J60, 32S20, 55R40, 05E15text