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(d2) then (X,L) admits a csck metric in the first chern class of L if and only if (X,L) is asymptotically stable.
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