# Kodaira dimension and the Yamabe problem

@article{Lebrun1997KodairaDA,
title={Kodaira dimension and the Yamabe problem},
author={Claude Lebrun},
journal={Communications in Analysis and Geometry},
year={1997},
volume={7},
pages={133-156}
}
• C. Lebrun
• Published 1997
• Mathematics
• Communications in Analysis and Geometry
The Yamabe invariant Y (M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalar curvature Riemannian metrics g on M . (To be absolutely precise, one only considers constant-scalar-curvature metrics which are Yamabe minimizers, but this does not affect the sign of the answer.) If M is the underlying smooth 4-manifold of a complex algebraic surface (M,J), it is shown that the sign of Y (M) is completely determined by the Kodaira dimension… Expand
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