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arXiv · 1302.0760

Blowing up extremal Kähler manifolds II

Gábor Székelyhidi
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Abstract

This is a continuation of the work of Arezzo-Pacard-Singer and the author on blowups of extremal Kähler manifolds. We prove the conjecture stated in [32], and we relate this result to the K-stability of blown up manifolds. As an application we prove that if a Kähler manifold M of dimension greater than 2 admits a 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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Gábor Székelyhidi. 2013-03-06. Blowing up extremal Kähler manifolds II. https://doi.org/10.1215/00127094-1593308

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