Let gS be the Simanca metric on the blow-up C~ 2 of C2 at the origin. We show that (C~ 2, gS) admits a regular quantization. We use this fact to prove that all coefficients in the Tian–Yau–Zelditch expansion for the Simanca metric vanish and that a dense subset of (C~ 2, gS) admits a Berezin quantization
