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.