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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 6, Pages 274–293 (Mi izv8412)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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.


DOI: https://doi.org/10.4213/im8412

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English version:
Izvestiya: Mathematics, 2016, 80:6, 1257–1274

Bibliographic databases:

Document Type: Article
UDC: 512.7+514.7+514.8
MSC: 53D12, 53D37, 53D50
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

Citation in format AMSBIB
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\vol 80
\issue 6
\pages 274--293
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\pages 1257--1274
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  • http://mi.mathnet.ru/eng/izv/v80/i6/p274

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Tyurin, “Special Bohr–Sommerfeld Lagrangian submanifolds of algebraic varieties”, Izv. Math., 82:3 (2018), 612–631  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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