Asian Journal of Mathematics

Volume 27 (2023)

Number 3

Spectral convergence in geometric quantization on $K3$ surfaces

Pages: 315 – 374



Kota Hattori (Keio University, Kohoku, Yokohama, Japan)


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 $\overline{\partial}$ Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr–Sommerfeld fibers.


geometric quantization, $K3$ surface, Bohr–Sommerfeld fiber, measured Gromov–Hausdorff convergence

2010 Mathematics Subject Classification

53D50, 58C40

Received 23 May 2022

Accepted 8 March 2023

Published 7 November 2023