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...The k ahler geometry of toric manifolds vestislav apostolov email address uqam ca contents preface acknowledgements chapter delzant theory hamiltonian group actions on symplectic tori complex projective space from polytopes varieties fans equivariant blow up polarized orbifolds abreu guillemin orbit a manifold metrics local scalar curvature versus legendre transform canonical metric compactication calabi problem and donaldson s futaki invariant uniqueness stability test congurations uniform existence an overview bibliography...