Jesus Martinez-Garcia
Published 2017-12-13Version 1
We show that the only projective smooth rational surfaces which admit a constant scalar curvature K\"ahler metric for all polarisations are the projective plane and the quadric surface. In particular, we show that all rational surfaces other than those two admit a destabilising slope test configuration, as introduced by Ross and Thomas. We further show that all Hirzebruch surfaces other than the quadric surface and all rational surfaces with Picard rank $3$ do not admit a constant scalar curvature K\"ahler metric for any polarisation.
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Du Val del Pezzo surfaces in positive characteristic
Pencils and nets of small degree on curves on smooth, projective surfaces of Picard rank 1 and very ample generator
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