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Blowing up Kähler manifolds with constant scalar curvature. II. (English) Zbl 1202.53069

Summary: We prove the existence of Kähler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold that already carries a constant scalar curvature Kähler metric. In the case where the manifold has nontrivial holomorphic vector fields with zeros, we give necessary conditions on the number and locations of the blow up points for the blow up to carry constant scalar curvature Kähler metrics.
For part I, cf. Acta Math. 196, 179–228 (2006; Zbl 1123.53036).

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
32Q15 Kähler manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)

Citations:

Zbl 1123.53036
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References:

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