Geodesic
Nontoric Foliations by Lagrangian Tori of Toric Fano Varieties
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 48-59

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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.
Mots-clés : foliation, Auroux foliation, Berezin symbol, moment map
Keywords: toric Fano variety, Lagrangian torus, Hamiltonian action of a symbol, geometric quantization. 
@article{MZM_2010_87_1_a5,
     author = {S. A. Belev and N. A. Tyurin},
     title = {Nontoric {Foliations} by {Lagrangian} {Tori} of {Toric} {Fano} {Varieties}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {48--59},
     publisher = {mathdoc},
     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a5/}
}
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S. A. Belev; N. A. Tyurin. Nontoric Foliations by Lagrangian Tori of Toric Fano Varieties. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 48-59. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a5/