Toric degenerations of integrable systems on Grassmannians and polygon spaces. (English) Zbl 1304.37037

Nohara, Yuichi; Ueda, Kazushi

Nagoya Math. J. 214, 125-168 (2014).

Authors’ abstract: We introduce a completely integrable system on the Grassmannian of \(2\)-planes in an \(n\)-space associated with any triangulation of a polygon with \(n\) sides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.

Reviewer: Manuel de León (Madrid)

MSC:

37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
53D37	Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
53D12	Lagrangian submanifolds; Maslov index
14M15	Grassmannians, Schubert varieties, flag manifolds

Keywords:

completely integrable systems; polygon triangulation; toric degeneration; Grassmannian space

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