The Simanca metric admits a regular quantization

Abstract

Let $g_S$ be the Simanca metric on the blow-up ${\tilde{\mathbb{C}}}^2$ of ${\mathbb{C}}^2$ at the origin. We show that $({\tilde{\mathbb{C}}}^2,g_S)$ 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 $({\tilde{\mathbb{C}}}^2,g_S)$ admits a Berezin quantization

17 pages. A new theorem and a new remark have been added