Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleEquivariant holomorphic embeddings from the complex projective line into a complex Grassmannian of 2-planes
PresenterIsami Koga (Kyushu University)
Author(s)Isami Koga and Yasuyuki Nagatomo
Sessionn/a
Time
Abstract


In this talk, we study a classification problem of $SU(2)$-equivariant
holomorphic embedding of complex projective line $\mathbb{C}P^1$ into a complex
Grassmannian of 2-planes $Gr_{n-2}(\mathbb{C}^n)$.
In order to classify such maps, we study holomorphic vector bundles over
$\mathbb{C}P^1$ of rank 2 with $SU(2)$-action, invariant metric and invariant
connection.
We classify such bundles and consequently we obtain the moduli space of
$SU(2)$-equivariant holomorphic maps.