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Izvestiya: Mathematics, 2016, Volume 80, Issue 6, Pages 1257–1274
DOI: https://doi.org/10.1070/IM8412 (Mi im8412) 		 
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
English version PDF (293 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM8412
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.
Funding agency Grant number
Russian Science Foundation 14-21-00053
This work is supported by the Russian Science Foundation under grant no. 14-21-00053.
Received: 19.05.2015
Revised: 29.09.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 6, Pages 274–293
DOI: https://doi.org/10.4213/im8412
Bibliographic databases:
Document Type: Article
UDC: 512.7+514.7+514.8
MSC: 53D12, 53D37, 53D50
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:376
    Russian version PDF:59
    English version PDF:24
    References:47
    First page:21
     
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