# Extremal K\"ahler metrics on blowups

@inproceedings{Dervan2021ExtremalKM, title={Extremal K\"ahler metrics on blowups}, author={Ruadha'i Dervan and Lars Martin Sektnan}, year={2021} }

Consider a compact Kähler manifold which either admits an extremal Kähler metric, or is a small deformation of such a manifold. We show that the blowup of the manifold at a point admits an extremal Kähler metric in Kähler classes making the exceptional divisor sufficiently small if and only if it is relatively K-stable, thus proving a special case of the Yau-Tian-Donaldson conjecture. We also give a geometric interpretation of what relative K-stability means in this case in terms of finite…

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