An application of Guillemin-Abreu theory to a non-abelian group action
Abstract
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 (n) action on n\0\. Using this framework we (re)construct a scalar-flat K\"ahler metric on the blow-up of n at the origin from data on the moment polytope.
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