Representing a point and the diagonal as zero loci in flag manifolds. (English) Zbl 07121520

Summary: 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.


57T20 Homotopy groups of topological groups and homogeneous spaces
55R25 Sphere bundles and vector bundles in algebraic topology
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