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

Kaji, Shizuo

doi:10.2140/agt.2019.19.2061

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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

DOI: 10.2140/agt.2019.19.2061

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.

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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

Volume 19, issue 4 (2019)