Scalar-flat Kahler surfaces of all genera

초록

Let (M,J) be a compact complex a-manifold which admits a Kahler metric for which the integral of the scalar curvature is non-negative. Also suppose that M does not admit a Ricci-flat Kahler metric. Then if M is blown up at sufficiently many points, the resulting complex surface ((M) over tilde,(J) over tilde) admits Kahler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16].

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