Nonstandard Lagrangian tori and pseudotoric structures
An important mathematical problem is the classification of Lagrangian tori or, more generally, of all possible Lagrangian submanifolds in symplectic manifolds up to a symplectomorphism or Hamiltonian isotopy. In the present paper, the author investigates twisted tori [\textit{Y. Chekanov} and \textit{F. Schlenk}, Electron. Res. Announc. Math. Sci. 17, 104--121 (2010; Zbl 1201.53083)], which are examples of exotic monotonic tori. The author shows that exotic Lagrangian tori constructed by Chekanov and Schlenk can be obtained for a large class of toric manifolds. For this, he translates their original construction into the language of pseudotoric structures. At the end of the paper, the author constructs, as an example, exotic Lagrangian tori on a del Pezzo surface of degree six, as an answer to the problem posed in [loc. cit.] of constructing nonstandard tori in \(\mathbb {CP}^2_3\) (the projective plane with three blown-up points).
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