1996/05/28 by Piotr Pragacz, Pragacz, Piotr
Computer Science · Mathematics · #05E15 #14C25 #14H40 #14J60 #14M15 #14N10 #32S20 #55R40 #57R20 05E05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #Mathematics and Applications #Polynomial and algebraic computation #Primary: 14C15 #Secondary: 14M12
paper · pdf · doi:10.48550/arxiv.alg-geom/9605014
openalex publication_date 1996/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.