Geometric quantization via SYZ transforms

Abstract

The so-called quantization problem in geometric quantization is asking whether the space of wave functions is independent of the choice of polarization. In this paper, we apply SYZ transforms to solve the quantization problem in two cases: (1) semi-flat Lagrangian torus fibrations over complete compact integral affine manifolds, and (2) projective toric manifolds. More precisely, we prove that the space of wave functions associated to the real polarization is canonically isomorphic to that associated to a complex polarization via SYZ transforms in both cases.

arXiv commentFinal version

References in corpus (5)

• Geometric quantization and mirror symmetry
• Toric Kähler metrics seen from infinity, quantization and compact tropical amoebas
• Holomorphic line bundles on projective toric manifolds from Lagrangian sections of their mirrors by SYZ transformations
• Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
• Lagrangian fibrations and theta functions

Cited by in corpus (1)

• Spectral convergence in geometric quantization on $K3$ surfaces