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This article is cited in 5 scientific papers (total in 5 papers)
Special Bohr–Sommerfeld Lagrangian submanifolds
N. A. Tyurinabc a Joint Institute for Nuclear Research, Dubna, Moscow region
b State University – Higher School of Economics
c Moscow State University of Railway Communications
Abstract:
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.
Received: 19.05.2015 Revised: 29.09.2015
Citation:
N. A. Tyurin, “Special Bohr–Sommerfeld Lagrangian submanifolds”, Izv. RAN. Ser. Mat., 80:6 (2016), 274–293; Izv. Math., 80:6 (2016), 1257–1274
Linking options:
https://www.mathnet.ru/eng/im8412https://doi.org/10.1070/IM8412 https://www.mathnet.ru/eng/im/v80/i6/p274
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Abstract page: | 376 | Russian version PDF: | 59 | English version PDF: | 24 | References: | 47 | First page: | 21 |
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