Xiuxiong Chen, Claude LeBrun, Brian Weber
Published 2007-05-07, updated 2007-05-30Version 2
We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex projective plane at two distinct points.
Comments: 45 pages, 9 figures. Simplified proof of Lemma 25. Several minor corrections to section 5
Einstein Metrics, Complex Surfaces, and Symplectic 4-Manifolds
Einstein metrics on connected sums of $S^2\times S^3$
On the nonexistence of Einstein metric on 4-manifolds
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