An application of Guillemin-Abreu theory to a non-abelian group action

Details An application of Guillemin-Abreu theory to a non-abelian group action An application of Guillemin-Abreu theory to a non-abelian group action

2004-10-22

arxiv.org/abs/math/0410484v4

Mathematics

Differential Geometry

8 pages. Part of submitted version

Scientific paper

This note is a step towards demonstrating the benefits of a symplectic approach to studying equivariant K\"ahler geometry. We apply a local differential geometric framework from K\"ahler toric geometry due to Guillemin & Abreu to the case of the standard linear $\SU(n)$ action on $\bbC^n\setminus\{0\}$. Using this framework we (re)construct a scalar-flat K\"ahler metric on the blow-up of $\bbC^n$ at the origin from data on the moment polytope.

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