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This article is cited in 1 scientific paper (total in 1 paper)
Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations
N. A. Tyurinabc a Joint Institute of Nuclear Research, Bogolyubov Theoretical Physics Laboratory
b National Research University "Higher School of Economics", Laboratory of Algebraic Geometry and Applications
c Moscow State University of Transport
Abstract:
This survey presents a generalization of the notion of a toric structure on a compact symplectic manifold: the notion of a pseudotoric structure. The language of these new structures appears to be a convenient and natural tool for describing many non-standard Lagrangian submanifolds and cycles (Chekanov's exotic tori, Mironov's cycles in certain particular cases, and others) as well as for constructing Lagrangian fibrations (for example, special fibrations in the sense of Auroux on Fano varieties). Known properties of pseudotoric structures and constructions based on these properties are discussed, as well as open problems whose solution may be of importance in symplectic geometry and mathematical physics.
Bibliography: 28 titles.
Keywords:
symplectic manifold, Lagrangian submanifold, Lagrangian fibration, toric manifold, Delzant polytope, exotic Lagrangian tori.
DOI:
https://doi.org/10.4213/rm9764
Full text:
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English version:
Russian Mathematical Surveys, 2017, 72:3, 513–546
Bibliographic databases:
UDC:
516.5
MSC: Primary 53D05, 53D12; Secondary 14M15, 14M25, 53D50 Received: 30.01.2017 Revised: 21.02.2017
Citation:
N. A. Tyurin, “Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations”, Uspekhi Mat. Nauk, 72:3(435) (2017), 131–169; Russian Math. Surveys, 72:3 (2017), 513–546
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/umn9764https://doi.org/10.4213/rm9764 http://mi.mathnet.ru/eng/umn/v72/i3/p131
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This publication is cited in the following articles:
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Nikolai A. Tyurin, “Monotonic Lagrangian Tori of Standard and Nonstandard Types in Toric and Pseudotoric Fano Varieties”, Proc. Steklov Inst. Math., 307 (2019), 267–280
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