Toric degenerations of weight varieties and applications

Research paper by Philip Foth, Yi Hu

Indexed on: 25 Jun '04Published on: 25 Jun '04Published in: Mathematics - Algebraic Geometry


We show that a weight variety, which is a quotient of a flag variety by the maximal torus, admits a flat degeneration to a toric variety. In particular, we show that the moduli spaces of spatial polygons degenerate to polarized toric varieties with the moment polytopes defined by the lengths of their diagonals. We extend these results to more general Flaschka-Millson hamiltonians on the quotients of products of projective spaces. We also study boundary toric divisors and certain real loci.