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

中文翻译：

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Simanca 度量承认常规量化

令 $g_S$ 是原点处 $\mathbb{C}^2$ 爆炸 $\tilde{\mathbb{C}}^2$ 的 Simanca 度量。我们证明 $(\tilde{\mathbb{C}}^2,g_S)$ 承认常规量化。我们使用这个事实来证明 Simanca 度量的 Tian-Yau-Zelditch 展开式中的所有系数都消失了，并且 $(\tilde{\mathbb{C}}^2, g_S)$ 的稠密子集承认了 Berezin 量化