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

Aleksis Raza
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Abstract

This note is a step towards demonstrating the benefits of a symplectic approach to studying equivariant Kähler geometry. We apply a local differential geometric framework from Kähler 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 Kähler metric on the blow-up of $\bbC^n$ at the origin from data on the moment polytope.

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Aleksis Raza. 2005-03-27. An application of Guillemin-Abreu theory to a non-abelian group action. https://arxiv.org/abs/math/0410484

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