Toric degenerations of integrable systems on Grassmannians and polygon spaces

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 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.

35 pages, 10 figures; v2: corrected an error pointed out by Harada and Escobar

References in corpus (2)

• Lagrangian Floer theory on compact toric manifolds I
• The Toric Geometry of Triangulated Polygons in Euclidean Space

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