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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 6 scientific papers (total in 6 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 (6) Russian version article
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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
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. Math., 80:6 (2016), 1257–1274
Citation in format AMSBIB
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\by N.~A.~Tyurin
\paper Special Bohr--Sommerfeld Lagrangian submanifolds
\jour Izv. Math.
\yr 2016
\vol 80
\issue 6
\pages 1257--1274
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Linking options:
  • https://www.mathnet.ru/eng/im8412
  • https://doi.org/10.1070/IM8412
  • https://www.mathnet.ru/eng/im/v80/i6/p274
    • This publication is cited in the following 6 articles:
    1. N. A. Tyurin, “Spetsialnaya geometriya Bora–Zommerfelda”, UMN, 80:2(482) (2025), 123–164  mathnet  crossref
    2. N. A. Tyurin, “Special Bohr–Sommerfeld geometry: variations”, Izv. Math., 87:3 (2023), 595–615  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. N. A. Tyurin, “On the Kählerization of the Moduli Space of Bohr–Sommerfeld Lagrangian Submanifolds”, Math. Notes, 107:6 (2020), 1038–1039  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Tyurin N.A., “Lagrangian Approach to Geometric Quantization”, Geometric Methods in Physics Xxxvii, Trends in Mathematics, ed. Kielanowski P. Odzijewicz A. Previato E., Birkhauser Verlag Ag, 2020, 255–258  mathscinet  isi
    5. N. A. Tyurin, “The moduli space of D-exact Lagrangian submanifolds”, Siberian Math. J., 60:4 (2019), 709–719  mathnet  crossref  crossref  isi  elib
    6. N. A. Tyurin, “Special Bohr–Sommerfeld Lagrangian submanifolds of algebraic varieties”, Izv. Math., 82:3 (2018), 612–631  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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:479
    Russian version PDF:78
    English version PDF:42
    References:74
    First page:21
     
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