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

Arezzo 2019 03 04

Claudio Arezzo
International Centre for Theoretical Physics, Trieste
March 4, 2019

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
of the resolved manifold will be discussed and the relevance towards the interpretation of the ADM mass for Kaehler
manifolds.The original part of this talk will cover joint works with A. Della Vedova, R. Lena, K. Corrales and L. Mazzieri.