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Representing a point and the diagonal as zero loci in flag manifolds

Shizuo Kaji

Algebraic & Geometric Topology 19 (2019) 2061–2075
Abstract

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.

Keywords
flag manifold, diagonal, Chern class
Mathematical Subject Classification 2010
Primary: 57T20
Secondary: 55R25
References
Publication
Received: 26 July 2018
Revised: 29 September 2018
Accepted: 9 December 2018
Published: 16 August 2019
Authors
Shizuo Kaji
Institute of Mathematics for Industry
Kyushu University
Fukuoka
Japan