Blowing up Kähler manifolds with constant scalar curvature, II

By C. Arezzo, Frank Pacard. 2005

88 citations recorded by the source corpus.

In this paper we prove the existence of Kahler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold that already carries a constant scalar curvature Kahler 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 Kahler metrics.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bdbdb47414d8bd63922261a0b13e60bb5c98d457

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Extremal metrics on blowups (2006, methodology): “The analysis inxx5{7 is very close to that of [ 1 , 2], and the reader is referred to these papers for a more detailed treatment.”
Notes on GIT and symplectic reduction for bundles and varieties (2005, result): “This of course involves some estimates, which is what [AP] work out for the cscK problem, to show that for aut = 0 there is always a cscK metric on the blow up.”
On the Calabi Flow (2006, methodology): “Around the same time, using method of gluing and grafting Arezzo-Pacard [2][3] were able to construct new CscK metrics on the blow up of manifold if the original manifold has a CscK metric.”