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## Seminars

### Representing the diagonal as the zero locus in a flag manifold

Hold Date
2018-06-29 16:00〜2018-06-29 17:00
Place
Lecture Room S W1-C-514, West Zone 1, Ito campus, Kyushu University
Object person

Speaker
Shizuo KAJI (Kyushu University)

Abstract:
Let $N$ be a manifold of dimension $2n$. Consider a smooth function $f: N\to \C^m$ having zero as its regular value. Then, $M=f^{-1}(0)\subset N$ is a sub-manifold of codimension $2m$. Conversely, we can ask if a sub-manifold $M\subset N$ of codimension $2m$ can be realised in this way, or more generally, as the zero locus of a generic section of a rank $m$ complex vector bundle over $N$. 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.