K-stability and parabolic stability

Yann Rollin (1)

1 Géométrie et analyse globale

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 scalar curvature Kähler metrics on the iterated blowup are equivalent, for certain polarizations close to the boundary of the Kähler cone.

Mots clés: Parabolic bundles; extremal metrics; Donadson-Tian-Yau conjecture; ruled surfaces

Domaines: Géométrie différentielle [math.DG]

Yann Rollin. K-stability and parabolic stability. 2013. ⟨hal-00798767v3⟩