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This article is cited in 10 scientific papers (total in 10 papers)
Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties
N. A. Tyurinab a Moscow State University of Railway Engineering (MIIT), Moscow, Russia
b Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia
Abstract:
We introduce the notion of a pseudotoric structure on a symplectic manifold, generalizing the notion of a toric structure. We show that such a pseudotoric structure can exist on toric and nontoric symplectic manifolds. For the toric manifolds, it describes deformations of the standard toric Lagrangian fibrations; for the nontoric ones, it gives Lagrangian fibrations with singularities that are very close to the toric fibrations. We present examples of toric manifolds with different pseudotoric structures and prove that certain nontoric manifolds (smooth complex quadrics) have such structures. In the future, introducing this new structure can be useful for generalizing the geometric quantization and mirror symmetry methods that work well in the toric case to a broader class of Fano varieties.
Keywords:
toric symplectic manifold, Lagrangian fibration, nondegenerate complex quadric, Bohr–Sommerfeld torus.
Received: 10.04.2009
Citation:
N. A. Tyurin, “Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties”, TMF, 162:3 (2010), 307–333; Theoret. and Math. Phys., 162:3 (2010), 255–275
Linking options:
https://www.mathnet.ru/eng/tmf6473https://doi.org/10.4213/tmf6473 https://www.mathnet.ru/eng/tmf/v162/i3/p307
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Abstract page: | 527 | Full-text PDF : | 206 | References: | 67 | First page: | 8 |
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