Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

TL;DR

This paper derives explicit formulas for degeneracy loci classes in vector bundles with symmetric or skew-symmetric maps, utilizing Schur Q-polynomials and push-forward techniques in Grassmann bundles.

Contribution

It introduces new closed-form formulas for degeneracy loci classes involving Schur Q-polynomials, extending previous methods to symmetric and skew-symmetric cases.

Findings

Formulas for degeneracy loci classes using Schur Q-polynomials

Application of push-forward formulas in Grassmann bundles

Explicit descriptions for symmetric and skew-symmetric matrix maps

Abstract

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.