Spectral convergence in geometric quantization on $K3$ surfaces

Abstract

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

To appear in The Asian Journal of Mathematics

References in corpus (2)

• Collapsing Ricci-flat metrics on elliptic K3 surfaces
• Spectral convergence in geometric quantization --- the case of toric symplectic manifolds