Toric degenerations of integrable systems on Grassmannians and polygon spaces
Symplectic Geometry
2019-07-05 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1111.4809,
title = {Toric degenerations of integrable systems on Grassmannians and polygon spaces},
author = {Yuichi Nohara and Kazushi Ueda},
journal= {arXiv preprint arXiv:1111.4809},
year = {2019}
}
Comments
35 pages, 10 figures; v2: corrected an error pointed out by Harada and Escobar