Geodesic
Special Bohr--Sommerfeld Lagrangian submanifolds
Izvestiya. Mathematics , Tome 80 (2016) no. 6, pp. 1257-1274

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We introduce a new notion in symplectic geometry, that of speciality for Lagrangian submanifolds satisfying the Bohr–Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr–Sommerfeld Lagrangian submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.
Keywords: symplectic manifold, Lagrangian cycle, Bohr–Sommerfeld condition, prequantization data, algebraic variety, speciality condition. 
@article{IM2_2016_80_6_a13,
     author = {N. A. Tyurin},
     title = {Special {Bohr--Sommerfeld} {Lagrangian} submanifolds},
     journal = {Izvestiya. Mathematics },
     pages = {1257--1274},
     publisher = {mathdoc},
     volume = {80},
     number = {6},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a13/}
}
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N. A. Tyurin. Special Bohr--Sommerfeld Lagrangian submanifolds. Izvestiya. Mathematics , Tome 80 (2016) no. 6, pp. 1257-1274. http://geodesic.mathdoc.fr/item/IM2_2016_80_6_a13/