The quotient of the Kodaira pullback Fubini-Study form by the Poincaré form near the punctures is O(p^3) as the tensor power p tends to infinity.
Catlin,The Bergman kernel and a theorem of Tian
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Fubini-Study forms on punctured Riemann surfaces
The quotient of the Kodaira pullback Fubini-Study form by the Poincaré form near the punctures is O(p^3) as the tensor power p tends to infinity.