Kodaira Dimension and the Yamabe Problem
| dc.creator | LeBrun, Claude | |
| dc.date | 1997-02-13 | |
| dc.date | 1997-02-18 | |
| dc.date.accessioned | 2026-07-07T09:02:52Z | |
| dc.date.available | 2026-07-07T09:02:52Z | |
| dc.description | 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 Kod (M,J). More precisely, Y(M) < 0 iff Kod (M,J)=2; Y(M) = 0 iff Kod (M,J)=0 or 1; and Y(M) > 0 iff Kod (M,J)= -infinity. | |
| dc.description | LaTeX file. With minor typographical errors corrected | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9702012 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9702012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148791 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.title | Kodaira Dimension and the Yamabe Problem | |
| dc.type | text |