منابع مشابه
Schubert complexes and degeneracy loci
The classical Thom–Porteous formula expresses the homology class of the degeneracy locus of a generic map between two vector bundles as an alternating sum of Schur polynomials. A proof of this formula was given by Pragacz by expressing this alternating sum as the Euler characteristic of a Schur complex, which gives an explanation for the signs. Fulton later generalized this formula to the situa...
متن کاملDouble Schubert polynomials and degeneracy loci for the classical groups
L’accès aux articles de la revue « Annales de l’institut Fourier » (http://aif.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://aif.cedram.org/legal/). Toute reproduction en tout ou partie cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute c...
متن کاملSchubert Polynomials and Degeneracy Locus Formulas
In previous work [T6], we employed the approach to Schubert polynomials by Fomin, Stanley, and Kirillov to obtain simple, uniform proofs that the double Schubert polynomials of Lascoux and Schützenberger and Ikeda, Mihalcea, and Naruse represent degeneracy loci for the classical groups in the sense of Fulton. Using this as our starting point, and purely combinatorial methods, we obtain a new pr...
متن کاملDegeneracy Loci in CR Geometry
Starting on the next page is the 16-page Chapter II excerpted from my dissertation, “Enumeration and Normal Forms for Singularities in CauchyRiemann Structures,” 1997, University of Chicago. I have made a few minor editorial modifications so that Chapter II can be read without referring to the other Chapters. Section 5 of Chapter II is a summary of results appearing in my unpublished lecture no...
متن کاملNonemptiness of Symmetric Degeneracy Loci
Let V be a renk N vector bundle on a d-dimensional complex projective scheme X; assume that V is equipped with a quadratic form with values in a line bundle L and that SV ∗ ⊗ L is ample. Suppose that the maximum rank of the quadratic form at any point of X is r > 0. The main result of this paper is that if d > N − r, the locus of points where the rank of the quadratic form is at most r − 1 is n...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.04.032