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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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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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