K-stability and parabolic stability
Résumé
Parabolic structures with rational weights encode certain iterated blowups of geometrically ruled surfaces. In this paper, we show that the three notions of parabolic polystability, K-polystability and existence of constant sca- lar curvature Ka ̈hler metrics on the iterated blowup are equivalent, for certain polarizations close to the boundary of the Kähler cone.
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