SCALAR-FLAT KAHLER SURFACES OF ALL GENERA

Authors
KIM J LEBRUN C PONTECORVO M
Citation
J. Kim et al., SCALAR-FLAT KAHLER SURFACES OF ALL GENERA, Journal fur die Reine und Angewandte Mathematik, 486, 1997, pp. 69-95
Citations number
30
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Journal fur die Reine und Angewandte Mathematik → ACNP
ISSN journal
00754102
Volume
486
Year of publication
1997
Pages
69 - 95
Database
ISI
SICI code
0075-4102(1997)486:<69:SKSOAG>2.0.ZU;2-6
Abstract
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 curva ture identically equal to zero. This proves Conjecture 1 of [16].