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Matematicheskie Zametki, 2010, Volume 87, Issue 1, Pages 48–59
DOI: https://doi.org/10.4213/mzm8548 (Mi mzm8548) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Nontoric Foliations by Lagrangian Tori of Toric Fano Varieties

S. A. Belevab, N. A. Tyurincb

a Moscow Institute of Physics and Technology
b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
c Moscow State University of Railway Communications
Full-text PDF (476 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm8548
Abstract: A construction of a foliation of a toric Fano variety by Lagrangian tori is presented; it is based on linear subsystems of divisor systems of various degrees invariant under the Hamiltonian action of distinguished function-symbols. It is shown that known examples of foliations (such as the Clifford foliation and D. Auroux's example) are special cases of this construction. As an application, nontoric Lagrangian foliations by tori of two-dimensional quadrics and projective space are constructed.
Keywords: foliation, toric Fano variety, Lagrangian torus, Auroux foliation, Berezin symbol, Hamiltonian action of a symbol, moment map, geometric quantization.
Received: 18.11.2008
Revised: 26.06.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 1, Pages 43–51
DOI: https://doi.org/10.1134/S0001434610010062
Bibliographic databases:
UDC: 514.8
Language: Russian
Citation: S. A. Belev, N. A. Tyurin, “Nontoric Foliations by Lagrangian Tori of Toric Fano Varieties”, Mat. Zametki, 87:1 (2010), 48–59; Math. Notes, 87:1 (2010), 43–51
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm8548
  • https://www.mathnet.ru/eng/mzm/v87/i1/p48
    • This publication is cited in the following 9 articles:
    1. Tiago Carvalho, Luiz Fernando Gonçalves, “Creation of Limit Cycles in Piecewise Smooth Vector Fields Tangent to Nested Tori”, Qual. Theory Dyn. Syst., 20:2 (2021)  crossref
    2. N. A. Tyurin, “Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations”, Russian Math. Surveys, 72:3 (2017), 513–546  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Carvalho T., Teixeira M.A., “On piecewise smooth vector fields tangent to nested tori”, J. Differ. Equ., 261:7 (2016), 4008–4029  crossref  mathscinet  zmath  isi  elib  scopus
    4. N. A. Tyurin, “Pseudotoric structures on a hyperplane section of a toric manifold”, Theoret. and Math. Phys., 182:2 (2015), 159–172  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. Tyurin N.A., “Exotic Chekanov Tori in Toric Symplectic Varieties”, Xxth International Conference on Integrable Systems and Quantum Symmetries (Isqs-20), Journal of Physics Conference Series, 411, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013, 012028  crossref  isi  scopus
    6. S. A. Belev, N. A. Tyurin, “Lifts of Lagrangian Tori”, Math. Notes, 91:5 (2012), 735–737  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. N. A. Tyurin, “Nonstandard Lagrangian tori and pseudotoric structures”, Theoret. and Math. Phys., 171:2 (2012), 700–703  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    8. N. A. Tyurin, “Chekanov tori and pseudotoric structures”, Russian Math. Surveys, 66:1 (2011), 181–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. N. A. Tyurin, “Special Lagrangian fibrations on the flag variety F3”, Theoret. and Math. Phys., 167:2 (2011), 567–576  mathnet  crossref  crossref  mathscinet  adsnasa  isi
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