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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.

MSC:

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