16 citations · 52 across the 9 of their papers we have counts for
9 papers
Potential functions on Grassmannians of planes and cluster transformations
Yuichi Nohara, Kazushi Ueda
With a triangulation of a planar polygon with sides, one can associate an integrable system on the Grassmannian of 2-planes in an -space. In this paper, we show that the pot…
Floer cohomologies of non-torus fibers of the Gelfand-Cetlin system
Yuichi Nohara, Kazushi Ueda
The Gelfand-Cetlin system has non-torus Lagrangian fibers on some of the boundary strata of the moment polytope. We compute Floer cohomologies of such non-torus Lagrangian fibers i…
Goldman systems and bending systems
Yuichi Nohara, Kazushi Ueda
We show that the moduli space of parabolic bundles on the projective line and the polygon space are isomorphic, both as complex manifolds and symplectic manifolds equipped with str…
Toric degenerations of integrable systems on Grassmannians and polygon spaces
Yuichi Nohara, Kazushi Ueda
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 fun…
Homological mirror symmetry for the quintic 3-fold
Yuichi Nohara, Kazushi Ueda
We prove homological mirror symmetry for the quintic Calabi-Yau 3-fold. The proof follows that for the quartic surface by Seidel (arXiv:math/0310414) closely, and uses a result of…
Potential functions via toric degenerations
Takeo Nishinou, Yuichi Nohara, Kazushi Ueda
This is a short companion paper to arXiv:0810.3470. We construct an integrable system on an open subset of a Fano manifold equipped with a toric degeneration, and compute the poten…