## Kaehler constant scalar curvature metrics on blow ups and resolutions of singularities

Abstract: After recalling the gluing construction for Kaehler constant scalar curvature and extremal (`a la Calabi) metrics

starting from a compact or ALE orbifolds with isolated singularities, I will show how to compute the Futaki invariant

of the adiabatic classes in this setting, extending previous work by Stoppa, Szekelyhidi and Odaka. Besides giving

new existence and non-existence results, the connection with the Tian-Yau-Donaldson Conjecture and the K-stability