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Asian Journal of Mathematics
Volume 27 (2023)
Number 3
Spectral convergence in geometric quantization on $K3$ surfaces
Pages: 315 – 374
DOI: https://dx.doi.org/10.4310/AJM.2023.v27.n3.a2
Author
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 $\overline{\partial}$ Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr–Sommerfeld fibers.
Keywords
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