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Title: Scalar curvature and multiplicity-free actions
Author: Raza, Aleksis
ISNI:       0000 0000 7193 4485
Awarding Body: Imperial College London (University of London)
Current Institution: Imperial College London
Date of Award: 2006
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This thesis comprises of three main results. First, we use Guillemin-Abreu theory from K�¤hler toric geometry to derive a formula for the scalar curvature of SU(n)-invariant K�¤hler 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, K�¤hler metric on the blow-up bCn of Cn at the origin in symplectic coordinates. This metric is the generalization of the well-known Burns metric on bC2. Third, we use an equivariant version of an ��infinite dimensional moment map framework�� to derive a formula for the scalar curvature of SU(n)-invariant, K�¤hler metrics on the multiplicity-free SU(n)-space Xn of the form SU(n) �£ U where U is a certain open connected subset of the Lie algebra of a Cartan torus in SU(n) i.e. Rn�¡1.
Supervisor: Donaldson Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available