Convergence of K\"ahler to real polarizations on flag manifolds via   toric degenerations
  In this paper we construct a family of complex structures on a complex flag manifold that converge to the real polarization coming from the Gelfand-Cetlin integrable system, in the sense that holomorphic sections of a prequantum line bundle converge to delta-function sections supported on the Bohr-Sommerfeld fibers. Our construction is based on a toric degeneration of flag varieties and a deformation of K\"ahler structure on toric varieties by symplectic potentials. 
Mark D. Hamilton, Hiroshi Konno
math.SG math.DG