Scalar curvature and multiplicity-free actions

Aleksis Raza
This thesis comprises of three main results. First, we use Guillemin-Abreu theory from Kähler toric geometry to derive a formula for the scalar curvature of SU(n)-invariant Kähler metrics on Cn n f0g or, equivalently, spaces of the form S2n¡1 £ (0,¥). Second, we use the aforementioned formula to describe a U(n)-invariant, scalar-flat, Kähler metric on the blow-up bCn of Cn at the origin in symplectic coordinates. This metric is the generalization of the well-known Burns...
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