Universal Schubert polynomials

TL;DR

The paper introduces universal Schubert polynomials that generalize classical and quantum Schubert polynomials, representing degeneracy loci for vector bundle maps, and proves their Cohen-Macaulay property.

Contribution

It defines universal Schubert polynomials for degeneracy loci, unifying classical and quantum cases, and proves their Cohen-Macaulay property in the universal setting.

Findings

Universal Schubert polynomials generalize classical and quantum forms.

Loci represented by these polynomials are Cohen-Macaulay.

The results unify and extend previous Schubert calculus theories.

Abstract

We introduce polynomials that represent general degeneracy loci for maps of vector bundles. These polynomials specialize to the known classical and quantum forms of single and double Schubert polynomials. This is the final version of the paper, to appear in Duke Math. J. The results are strengthened because Lakshmibai and Magyar have proved a conjecture from the previous version: in the universal case, these loci are Cohen-Macaulay.