Toric degenerations of integrable systems on Grassmannians and polygon spaces

Details Toric degenerations of integrable systems on Grassmannians and polygon spaces Toric degenerations of integrable systems on Grassmannians and polygon spaces

2011-11-21

arxiv.org/abs/1111.4809v1

Mathematics

Symplectic Geometry

41 pages, 10 figures

Scientific paper

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 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.

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