Abstract
In this paper 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.
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[Are-Pac]
C. Arezzo and F. Pacard, "Blowing up and desingularizing constant scalar curvature Kähler manifolds," Acta Math., vol. 196, iss. 2, pp. 179-228, 2006.@article {Are-Pac, MRKEY = {2275832},
AUTHOR = {Arezzo, Claudio and Pacard, Frank},
TITLE = {Blowing up and desingularizing constant scalar curvature {K}ähler manifolds},
JOURNAL = {Acta Math.},
FJOURNAL = {Acta Mathematica},
VOLUME = {196},
YEAR = {2006},
NUMBER = {2},
PAGES = {179--228},
ISSN = {0001-5962},
CODEN = {ACMAA8},
MRCLASS = {32J27 (32Q15 32Q20 53C21 53C55)},
MRNUMBER = {2007i:32018},
MRREVIEWER = {Julien Keller},
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} -
[Are-Pac-3] Arezzo, Claudio and Pacard, Frank, On the Kähler classes of constant scalar curvature metrics on blow ups.
@unpublished{Are-Pac-3,
author = {Arezzo, Claudio and Pacard, Frank},
TITLE={On the Kähler classes of constant scalar curvature metrics on blow ups},
NOTE={arXiv:0706.1838},
} -
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