Corpus ID: 119314043

Constant scalar curvature Kähler metrics on rational surfaces

  title={Constant scalar curvature K{\"a}hler metrics on rational surfaces},
  author={J. Mart{\'i}nez-Garc{\'i}a},
  journal={arXiv: Algebraic Geometry},
  • J. Martínez-García
  • Published 2017
  • Mathematics
  • arXiv: Algebraic Geometry
  • We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kahler metric for every Kahler class. We show that there are only two such rational surfaces, namely 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 for some polarization, as introduced by Ross and Thomas. We further show that all Hirzebruch… CONTINUE READING
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