The zero locus of a generic section of a vector bundle over a manifold defines a submanifold. A classical problem in geometry asks to realise a specified submanifold in this way. We study two cases: a point in a generalised flag manifold and the diagonal in the direct product of two copies of a generalised flag manifold. These cases are particularly interesting since they are related to ordinary and equivariant Schubert polynomials, respectively.
"Representing a point and the diagonal as zero loci in flag manifolds." Algebr. Geom. Topol. 19 (4) 2061 - 2075, 2019. https://doi.org/10.2140/agt.2019.19.2061