Geometric quantization and mirror symmetry
arXiv:math/9902027
Abstract
After the appearance of my preprint [T3] (Special Lagrangian geometry and slightly deformed algebraic geometry (spLag and sdAG), Warwick preprint 22/1998, alg-geom/9806006, 54 pp.). I received an e-mail from Cumrun Vafa, who recognized that the subject is closely related to that of his preprint [V] (Extending mirror conjecture to Calabi-Yau with bundles, hep-th/9804131, 7 pp.). This text started out as an e-mail ``reply'' to his letter. All the constructions we propose have well known ``spectral curve'' prototypes (see for example Friedman and other [FMW], Bershadsky and other [BJPS] and a number of others). Roughly speaking, our constructions are the spectral curve construction plus the phase geometry described in [T3]. So this text should really come before [T3], as motivation for the development of the geometry of the phase map in [T3].
latex2e with amsmath, amsfonts, amssymb, theorem, 53 pages
References in corpus (5)
Cited by in corpus (14)
- The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications
- Mirror symmetry and actions of braid groups on derived categories
- Mirror symmetry for log Calabi-Yau surfaces I
- On Bohr-Sommerfeld bases
- Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
- Complexification of Bohr-Sommerfeld conditions
- Quantization and ``theta functions''
- Geometric quantization via SYZ transforms
- Maslov class of lagrangian embedding to Kahler manifold
- Lagrangian fibrations and theta functions
- Spectral convergence in geometric quantization on surfaces
- Hamiltonian dynamics on the moduli space of half weighted Bohr - Sommerfeld Lagrangian subcycles of a fixed volume
- Compactification of the moduli of polarized abelian varieties and mirror symmetry
- Three conjectures on lagrangian tori in the projective plane