Convergence of Kähler to real polarizations on flag manifolds via toric degenerations

Details Convergence of Kähler to real polarizations on flag manifolds via toric degenerations Convergence of Kähler to real polarizations on flag manifolds via toric degenerations

2011-05-04

arxiv.org/abs/1105.0741v1

Mathematics

Symplectic Geometry

30 pages

Scientific paper

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.

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