Monotonic Lagrangian Tori of Standard and Nonstandard Types in Toric and Pseudotoric Fano Varieties


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In recent papers we constructed examples of nonstandard Lagrangian tori in compact simply connected toric symplectic manifolds. Using a new “pseudotoric” technique, we explained the appearance of nonstandard Lagrangian tori of Chekanov type and proposed a topological obstruction which separates them from the standard ones. In the present paper we construct nonstandard tori satisfying the Bohr-Sommerfeld condition with respect to the anticanonical class. Then we prove that if there exists a standard monotonic Lagrangian torus in a smooth simply connected toric Fano variety equipped with a canonical symplectic form, then there must exist a monotonic Lagrangian torus of Chekanov type.

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Nikolai Tyurin

Bogoliubov Laboratory of Theoretical Physics; Steklov Mathematical Institute of Russian Academy of Sciences

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Email: ntyurin@theor.jinr.ru
俄罗斯联邦, Dubna, Moscow region, 141980; ul. Gubkina 8, Moscow, 119991

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