Journal of Symplectic Geometry
Volume 12 (2014)
Convergence of Kähler to real polarizations on flag manifolds via toric degenerations
Pages: 473 – 509
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 Kähler structure on toric varieties by symplectic potentials.