Special Bohr-Sommerfeld Lagrangian submanifolds

Special Bohr-Sommerfeld Lagrangian submanifolds

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 bun...

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Veröffentlicht in:Izvestiya. Mathematics 2016-01, Vol.80 (6), p.1257-1274
1. Verfasser: Tyurin, N. A.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
algebraic variety
Bohr-Sommerfeld condition
Bundling
Lagrangian cycle
Manifolds (mathematics)
Mathematical analysis
prequantization data
speciality condition
Symmetry
symplectic manifold
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Beschreibung
Zusammenfassung: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.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM8412