Abstract
This is a continuation of the work of Arezzo–Pacard–Singer and the author on blowups of extremal Kahler manifolds. We prove the conjecture stated in Szekelyhidi (Duke Math J 161(8):1411–1453, 2012), and we relate this result to the K-stability of blown up manifolds. As an application we prove that if a Kahler manifold $$M$$ of dimension $$>$$ 2 admits a constant scalar curvature (cscK) metric, then the blowup of $$M$$ at a point admits a cscK metric if and only if it is K-stable, as long as the exceptional divisor is sufficiently small.
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