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arXiv 2016-01-22 0 views

Lagrangian shadows of ample algebraic divisors

Tyurin, Nikolay A.

Original · EN

In the framework of Special Bohr - Sommerfeld geometry it was established that an ample divisor in compact algebraic variety can define almost canonically certain real submanifold which is lagrangian with respect to the corresponding Kahler form. It is natural to call it "lagrangian shadow"; below we emphasize this correspondence and present some simple examples, old and new. In particular we show that for irreducible divisors from the linear system - 1/2 KF₃ on the full flag variety F³ their lagrangian shadows are Gelfand - Zeytlin type lagrangian 3 - spheres.

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