Geodesic
Blowing up Kähler manifolds with constant scalar curvature, II
Claudio Arezzo1 ; Frank Pacard2
1Università di Parma<br/>Parco delle Scienze 45/A<br/>43100 Parma<br/>Italy
2Institut Universitaire de France and Université Paris 12 - Val de Marne<br/>61, avenue du Général de Gaulle<br/>94010 Créteil<br/>France
Annals of mathematics, Tome 170 (2009) no. 2, pp. 685-738
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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.

DOI : 10.4007/annals.2009.170.685

Claudio Arezzo  1   ; Frank Pacard  2

1 Università di Parma<br/>Parco delle Scienze 45/A<br/>43100 Parma<br/>Italy
2 Institut Universitaire de France and Université Paris 12 - Val de Marne<br/>61, avenue du Général de Gaulle<br/>94010 Créteil<br/>France 
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     author = {Claudio Arezzo and Frank Pacard},
     title = {Blowing up {K\"ahler} manifolds with constant scalar curvature, {II}},
     journal = {Annals of mathematics},
     pages = {685--738},
     year = {2009},
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     number = {2},
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     zbl = {1202.53069},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.685/}
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Claudio Arezzo; Frank Pacard. Blowing up Kähler manifolds with constant scalar curvature, II. Annals of mathematics, Tome 170 (2009) no. 2, pp. 685-738. doi: 10.4007/annals.2009.170.685

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