Faltings Heights, Igusa Local Zeta Functions, and the Stability Conjectures in Kahler Geometry I

Abstract

Let (X,L) be a polarized manifold. Assume that the automorphism group is finite. If the height discrepancy of (X,L) is O(d^2) then (X,L) admits a csck metric in the first chern class of L if and only if (X,L) is asymptotically stable.

References in corpus (3)

• On the constant scalar curvature Kähler metrics, existence results
• On the constant scalar curvature Kähler metrics, general automorphism group
• On the constant scalar curvature Kähler metrics, apriori estimates