J. Ross
Published 2005-06-22, updated 2005-08-24Version 3
We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the work of Song-Weinkove on the J-flow.
Comments: Added implications for unstable Hilbert and Chow points; typos corrected
Constant scalar curvature Kahler metrics on rational surfaces
Irreducibility of the Hilbert scheme of smooth curves in $\Bbb P^4$ of degree $g+2$ and genus $g$
The Equivalence of Hilbert and Mumford Stability for Vector Bundles
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