Architectonics of Alain Lascoux's preferred formulas. (Architectonique des formules préférées d'Alain Lascoux.)
Cycles of isotropic subspaces and formulas for symmetric degeneracy loci
Symmetric polynomials and divided differences in formulas of intersection theory
The goal of this paper is at least two-fold. First we attempt to give a survey of some recent (and developed up to the time of the Banach Center workshop Parameter Spaces, February '94) applications of the theory of symmetric polynomials and divided differences to intersection theory. Secondly, taking this opportunity, we complement the story by either presenting some new proofs of older results (and this takes place usually in the Appendices to the present paper) or providing some new results which...
Enumerative geometry of degeneracy loci
Thom polynomials and Schur functions: the singularities
We give the Thom polynomials for the singularities associated with maps with parameter . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.
A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians.
Pieri Type formula for isotropic Grassmannians; the operator approach.
Polynomials homologically supported on degeneracy loci
A Pieri-type formula for even orthogonal Grassmannians
We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...
Positivity of Schur function expansions of Thom polynomials
Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.
On the class of Brill-Noether loci for Prym varieties.
Positivity of Thom polynomials II: the Lagrange singularities
We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.
Page 1