Blowing up Kähler manifolds with constant scalar curvature, II


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.


Claudio Arezzo

Università di Parma
Parco delle Scienze 45/A
43100 Parma

Frank Pacard

Institut Universitaire de France and Université Paris 12 - Val de Marne
61, avenue du Général de Gaulle
94010 Créteil