Inventiones mathematicae

, Volume 200, Issue 3, pp 925–977 | Cite as

Blowing up extremal Kähler manifolds II

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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 Székelyhidi (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 Kähler 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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Notes

Acknowledgments

I would like to thank Frank Pacard and Michael Singer for several useful discussions.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA

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