It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high $p$-tensor powers of the prequantum line bundle. We show that the Fubini-Study metrics induced by these embeddings converge at speed rate $1/p^{2}$ to the symplectic form.

中文翻译：

---

辛流形上伯格曼度量的最优收敛速度

已知具有前量子线丛的紧凑辛流形可以嵌入由博赫纳拉普拉斯算子的低能量本征截面作用于前量子线丛的高 $p$-张量幂而产生的射影空间中。我们表明，由这些嵌入引起的 Fubini-Study 指标以 $1/p^{2}$ 的速度收敛到辛形式。