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We study the geometric quantization on $K3$ surfaces from the viewpoint ofthe spectral convergence. We take a special Lagrangian fibrations on the $K3$surfaces and a family of hyper-K\"ahler structures tending to large complexstructure limit, and show a spectral convergence of the$\bar{\partial}$-Laplacians on the prequantum line bundle to the spectralstructure related to the set of Bohr-Sommerfeld fibers.

Spectral convergence in geometric quantization on $K3$ surfaces