Positivity of quiver coefficients through Thom Polynomials

We use the Thom Polynomial theory developed by Feher and Rimanyi to prove the component formula for quiver varieties conjectured by Knutson, Miller, and Shimozono. This formula expresses the cohomology class of a quiver variety as a sum of products of Schubert polynomials indexed by minimal lace diagrams, and implies that the quiver coefficients of Buch and Fulton are non-negative. We also apply our methods to give a new proof of the component formula from the Grobner degeneration of quiver varieties, and to give generating moves for the KMS-factorizations that form the index set in K-theoretic versions of the component formula. (c) 2004 Elsevier Inc. All rights reserved.